# Difference between revisions of "Bibliography"

### Important note

This bibliography was ported over from the previous incarnation of these pages. It should now be considered obsolete. Instead, we are now giving each reference its own page.

The naming system for these articles was somewhat implicit and ad hoc; we are currently forming more explicit standards for this.

### References

A

Aa2002 M. Aassilla, Nonexistence de solutions globales de certains equations d'ondes nonlineaires, C. R. Acad. Sci. Paris. 334 (2002), 961-966.

AbdBnFelSau1989 L. Abdelouhab, J. Bona, M. Felland, J. Saut, Nonlocal models for nonlinear dispersive waves, Phys. D 40 (1989), 360-392.

AbKauNeSe1974 M. Ablowitz, D. Kaup, A. Newell, H. Segur, The inverse scattering transform-Fourier analysis for nonlinear problems, Studies in Appl. Math. 53 (1974), no. 4, 249-315.

AbFs1983 M. Ablowitz, A. Fokas, The inverse scattering transform for the Benjamin-Ono equation, a pivot for multidimensional problems, Stud. Appl. Math. 68 (1983), 1-10.

AbHab1975 M. Ablowitz, R. Haberman, Nonlinear evolution equations in two and three dimensions, Phys. Rev. Lett. 35 (1975), 1185-1188.

AbMa1981 M. Ablowitz, Y. Ma, The periodic nonlinear Schrodinger equation, Stud. Appl. Math. 65 (1981), 113-158.

AbSe1977 M. Ablowitz, H. Segur, Asymptotic solutions of the Korteweg de Vries equation, Stud. Appl. Math. 57 (1977), 13-44.

AdhAds1988 H. Added, S. Added, Equations of Langmuir turbulence and non-linear Schrodinger equation: Smoothness and approximations, JFA 79 (1988), 183-210.

AgYok1998 R. Agemi, K. Yokoyama, The null condition and global existence of solutions to systems of wave equations with different speeds, Adv. Nonlinear PDE and Stochastics (1998), 43-86.

AxPgSac1997 J.C. Alexander, R.L. Pego, R.L. Sachs, On the transverse instability of solitary waves in the Kadomtsev-Petviashvili equation, Phys. Lett. A. 226 (1997), 187-192.

Al1995 S. Alinhac, Blowup for nonlinear hyperbolic equations, Boston: Birkhauser, 1995, Progress in Nonlinear DE and their Applications, 17.

Al1999 S. Alinhac, Blow up of small data solutions for a class of quasilinear wave equations in two space dimensions I, Annals of Mathematics 149 (1999), 97-127.

Al1999b S. Alinhac, Blow up of small data solutions for a class of quasilinear wave equations in two space dimensions II, Acta Math. 182 (1999), 1-23.

Al2000 S. Alinhac, Rank 2 singular solutions for quasilinear wave equations, IMRN 18 (2000), 955-984.

Al2001 S. Alinhac, The null condition for quasilinear wave equations in two space dimensions I, Invent. Math. 145 (2001), 597-618.

Al2001b S. Alinhac, The null condition for quasilinear wave equations in two space dimensions II, AJM 123 (2001), 1071-1101.

Al2003 S. Alinhac, An example of blowup at infinity for a quasilinear wave equation, Asterisque 284 (2003), 1-91.

AcIb2000 S. Anco, J. Isenberg, Global existence for wave maps with torsion, CPDE 25 (2000), 1669-1702.

AnMc-p L. Andersson, V. Moncrief, Elliptic-Hyperbolic systems and the Einstein equations, preprint.

Ant2003 C. Antonini, Lower bounds for the L^2 minimal periodic blowup solutions of critical nonlinear Schrodinger equation, DIE 15 (2002), 749-768.

AntMe2001 C. Antonini, F. Merle, Optimal bounds on positive blowup solutions for a semilinear wave equation, IMRN 21 (2001), 1143-1167.

ArYa2000 G. Artbazar, K. Yajima, The L^p continuity of wave operators for one dimensional Schrodinger operators, J. Math. Sci. Univ. Tokyo 7 (2000), 221-240.

AsCoeWgg1996 J. M. Ash, J. Cohen, G. Wang, On strongly interacting internal solitary waves, J. Fourier Anal. Appl., 2 (1996), 507-517.

B

Bch1984 A. Bachelot, Probleme de Cauchy pour des systemes hyperboliques semilineaires, Ann. IHP (Anal. nonlin), 1 (1984), 453-478.

BchNic1993 A. Bachelot, J-P. Nicolas, Equation non-lineaire de Klein-Gordon dans des metriquesde type Schwarzchild, C.R. Acad. Sci. Paris. 316 (1993), 1047-1050

BlChd1978 J. B. Baillon, J. M. Chadam, The Cauchy problem for the coupled Schrodinger-Klein-Gordon equations, in "Contemporary Developments in Continuum Mechanics and Partial Differential Equations", G. M. de La Penha and L. A. Medeiros eds., North Holland, Amsterdam 1978

BaeSgZz1990 J. Baez, I. Sega, Z. Zhou, The global Goursat problem and scattering for nonlinear wave equations, J. Funct. Anal. 93 (1990), 239-269.

BaCh1999 H. Bahouri, J-Y. Chemin, Équations d'ondes quasilinéaires et les inegalites de Strichartz, Amer. J. Math.121 (1999), 1337-1377.

BaCh1999b H. Bahouri, J-Y. Chemin, Équations d'ondes quasilinéaires et effet dispersif, IMRN 21 (1999), 1141-1178.

BaCh2002 H. Bahouri, J-Y. Chemin, Quasilinear Wave equations and Microlocal Analysis, ICM 2002, Vol III, 141-154.

BaCh-p H. Bahouri, J-Y. Chemin, Microlocal analysis, bilinear estimates, and cubic quasilinear wave equation, preprint.

BaGd1997 H. Bahouri and P.Gerard, High frequency approximation of solutions to critical nonlinear wave equations, Prepublications 97-34, Universite de Paris-Sud, Mai 1997. Appeared in: Amer. J. Math 121 (1999), 131-175.

BaGdXu2000 H. Bahouri, P. Gerard, C. Xu, Espaces de Besov et estimations de Strichartz generalisees sur le groupe de Heisenberg, Journal d'Analyse Mathematique 82 (2000), 93-118.

BaSa1998 H. Bahouri and J.Shatah, Decay estimates for the critical semilinear wave equation, Ann. Inst. H. Poincare Anal. Non Lineaire 15 (1998), no. 6, 783-789.

Ban-p V. Banica, On the nonlinear Schrodinger dynamics on S^2, preprint.

Ban-p2 V. Banica, Dispersion and Strichartz inequalities for Schrodinger equations with singular coefficients, preprint.

Bb1984 J.E. Barab, Nonexistence of asymptotically free solutions for a nonlinear Schrodinger equation, J. Math. Phys. 25 (1984), 3270-3273.

Be1983 M. Beals, Self-Spreading and strength of Singularities for solutions to semilinear wave equations, Annals of Math 118 (1983), 187-214

BeBz1996 M. Beals, M. Bezard, Low regularity local solutions for field equations, Comm. Partial Differential Equations21 (1996), 79-124.

BecMauSb-p P. Bechouce, N. Mauser, S. Selberg, Nonrelativistic limit of Klein-Gordon-Maxwell to Schrodinger Poisson, preprint

BecMauSb-p2 P. Bechouce, N. Mauser, S. Selberg, On the asymptotic analysis of the Dirac-Maxwell system in the nonrelativistic limit, preprint

BkOgPo1996 D. Bekiranov, T. Ogawa, G. Ponce, On the well-posedness of Benney's interaction equation of short and long waves, Adv. Diff. Eq. 1 (1996), 919-937.

BkOgPo1997 D. Bekiranov, T. Ogawa, G. Ponce, Weak solvability and well-posedness of the coupled Schrodinger Korteweg-de Vries equation in the capillary-gravity interaction waves, Proc. Amer. Math. Soc. 125 (1997), 2907-2919.

BkOgPo1998 D. Bekiranov, T. Ogawa, G. Ponce, Interaction equations for short and long dispersive waves, J. Funct. Anal. 158 (1998), 357-388.

BcKkZz1999 E. Belchev, M. Kepka, Z. Zhou, Global existence of solutions to nonlinear wave equations, CPDE 24 (1999), 2297-2331.

BcKkZz2002 E. Belchev, M. Kepka, Z. Zhou, Finite time blowup of solutions to semilinear wave equations, JFA 190 (2002), 233-254.

Bj1967 T. Benjamin, Internal waves of permanent form in fluids of great depth, J. Fluid Mech. 29 (1967), 559-562.

Bj1972 T. Benjamin, The stability of solitary waves, Proc. R. Soc. Lond. A. 328 (1972), 153-183.

BjBnMah1972 T. Benjamin, J. Bona, J. Mahony, Model equations for long waves in nonlinear dispersive systems, Phil. Trans. R. Soc. London A 272 (1972), 47-78.

BenKl1992 M. Ben-Artzi, S. Klainerman, Decay and regularity for the Schrodinger equation, J. Anal. Math. 58 (1992), 25-37.

BenSau1999 M. Ben-Artzi, J.C. Saut, Uniform decay estimates for a class of oscillatory integrals and applications, Diff. Int. Eq. 12 (1999), 137-145.

BenKocSau2003 M. Ben-Artzi, H. Koch, J.C. Saut, Dispersion estimates for third order equations in two dimensions, CPDE 28 (2003), 1943-1974.

ByNe1967 D.J. Benney, A.C. Newell, The propagation of nonlinear wave envelopes, J. Math. and Phys. 46 (1967), 133-139.

BerCa1981 H. Berestycki, T. Cazenave, Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaires, C. R. Acad. Sc. Paris, t. 293 (1981), 489-492.

BgCcMc1995 B.K. Berger, P. T. Chrusciel, V. Moncrief, On "asymptotically flat" spacetimes with G_2 invariant Cauchy surfaces, Ann. Physics 237 (1995), 322-354.

• linares.ps BiLi-p H. Biagioni, F. Linares, [linares.ps Ill-posedness for the Derivative Schrodinger and Generalized Benjamin-Ono equations], preprint.

BirPoVe-p B. Birnir, G. Ponce, L. Vega, On the ill-posedness for the initial value problem for the modified Korteweg-de Vries equation, preprint.

BirKnPoSvVe1996 B. Birnir, C. Kenig, G. Ponce, N. Svanstedt, L. Vega, On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations. J. London Math. Soc. (2) 53 (1996), 551-559.

Biz2000 P. Bizon, Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere. Comm. Math. Phys. 215 (2000), 45-56.

Biz-p P. Bizon, Formation of singularities in Yang-Mills equations, preprint

BizCjTb2001 P. Bizon, T. Chmaj, Z. Tabor, Formation of singularities for equivariant 2+1 dimensional wave maps into two-sphere, Nonlinearity 14 (2001), no. 5, 1041-1053.

BizOvSi-p P. Bizon, Y. Ovchinnikov, I. Sigal, Collapse of an Instanton, preprint.

BizTb2001 P. Bizon, Z. Tabor, On blowup for Yang-Mills fields, Phys. Rev. D (3) 64 (2001), 121701.

BluSf2003 P. Blue, A. Soffer, Semilinear wave equations on the Schwarzschild manifold I.Local decay estimates, Adv. Diff Eq. 8 (2003), 595-614.

Bn1975 J. Bona, On the stability theory of solitary waves, Proc. R. Soc. Lond. A. 344 (1975), 363-374.

BnDgKar1986 J. Bona, V.A. Dougalis, O.A. Karakashian, Fully discrete Galerkin methods for the Korteweg-de Vries equation, Comput. Math. Appl. Ser. A 12 (1986), 859-884.

BnLiu2002 J. Bona, Y. Liu, Instability of solitary-wave solutions of the Kadomtsev-Petviashvili equation in three dimensions, ADE 7 (2002), 1-33.

BnPoSauTm1992 J. Bona, G. Ponce, J-C. Saut, M. Tom, A model system for strong interaction between internal solitary waves, CMP 143 (1992), 287-313.

BnSco1976 J. Bona, R. Scott, Solutions of the Korteweg-de Vries equation, in fractional order Sobolev spaces, Duke Math J. 43 (1976), 87-99.

BnSmr1975 J. Bona, R. Smith, The initial-value problem for the Korteweg-de Vries equation, Philos. Trans. Royal Soc. London Series A 278 (1975), 555-601.

BnSouSr1987 J. Bona, P.E. Sougandis, W. Strauss, Stability and instability of solitary waves of Korteweg-de Vries type, Proc. R. Soc. Lond. 411 (1987), 395-412.

BnSuZh-p J. Bona, S. Sun, B-Y. Zhang, A non-homogeneous boundary-value problem for the Korteweg-de Vries Equation in a Quarter Plane, preprint

BnWi1983 J. Bona, R. Winther, The Korteweg-de Vries equation, posed in a quarter plane, SIAM J. Math. Anal. 14 (1983), 1056-1106.

BnWe-p J. Bona, F. B. Weissler, Similarity solutions of the generalized Korteweg-de Vries equations, preprint.

Bd1993 A. de Bouard, Analytic solutions to nonelliptic nonlinear Schrodinger equations, JDE 104 (1993), 196-213.

BdDbTs1999 A. de Bouard, A. Debussche, Y. Tsutsumi, White noise driven Korteweg-de Vries equation. J. Funct. Anal. 169 (1999), no. 2, 532-558

BdSau1997 A. de Bouard, J.C. Saut, Solitary waves of generalized Kadomtsev-Petviashvili equations, Annales IHP, Analyse non-lineaire 14 (1997) 211-236.

BdHaSau1997 A. de Bouard, N. Hayashi, J.C. Saut, Global existence of small solutions to a nonlinear relativistic Schrodinger equation, CMP 189 (1997), 73-105.

BdMt2004 A. de Bouard, Y. Martel, Nonexistence of L^2-compact solutions of the Kadomptsev-Petviashvili II equation, Math. Ann. 328 (2004), 525\u2014554.

BctGolPal-p F. Bouchut, F. Golse, C. Pallard, On classical solutions to the 3D relativistic Vlasov-Maxwell system: Glassey-Strauss's theorem revisited, preprint.

Bo1992 J. Bourgain, A remark on Schrodinger operators, Israel J. Math. 77 (1992), 1-16.

Bo1993 J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I. Schrodinger equations, Geom. Funct. Anal. 3 (1993) 107-156.

Bo1993b J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations II. The periodic KdV equation, Geom. Funct. Anal. 3 (1993) 209-262.

Bo1993c J. Bourgain, On the Cauchy problem for the Kadomtsev-Petviashvili equation, Geom. Funct. Anal. 3 (1993) 315-341.

Bo1993d J. Bourgain, Exponential sums and nonlinear Schrodinger equations, Geom. Funct. Anal. 3 (1993) 157-178.

Bo1994 J. Bourgain, On the Cauchy and invariant measure problem for the periodic Zakharov system, Duke Math. J. 76 (1994), 175-202.

Bo1994b J. Bourgain, Harmonic analysis and nonlinear partial differential equations, Proceedings of the ICM 1994, 31-44, Birkhauser Basel, 1995.

Bo1994c J. Bourgain, Periodic nonlinear Schrodinger equation and invariant measures, CMP 166 (1994), 1-26.

Bo1995 J. Bourgain, Estimates for cone multipliers, Operator Theory: Advances and Applications, 77 (1995), 41-60.

Bo1995b J. Bourgain, Aspects of longtime behaviour of solutions of nonlinear Hamiltonian evolution equations, GAFA 5 (1995), 105-140.

Bo1995c J. Bourgain, Periodic nonlinear Schrodinger equations and invariant measures, CMP 166 (1995), 1-26.

Bo1996 J. Bourgain, On well-posedness of the Zakharov system, Int. Math. Research Notices 11 (1996), 515-546.

Bo1996b J. Bourgain, Invariant measures for the 2d-defocussing nonlinear Schrodinger equation, Comm. Math. Phys. 176 (1996), 421-445.

Bo1996c J. Bourgain, On the growth in time of higher order Sobolev norms of smooth solutions of Hamiltonian PDE, IMRN 6 (1996), 277-304.

• kdv_measures.pdf Bo1997 J. Bourgain, [kdv_measures.pdf Periodic Korteweg de Vries equation with measures as initial data], Selecta Math. (N.S.) 3 (1997), 115-159.

Bo1997b J. Bourgain, On the compactness of support of solutions of dispersive equations, Int. Math. Research Notices 9 (1997), 437-447.

Bo1998 J. Bourgain, Refinements of Strichartz' inequality and applications to 2D-NLS with critical non-linearity, Int. Math. Research Notices, 5 (1998), 253-283.

Bo1998b J. Bourgain, Scattering in the energy space and below for 3D NLS, J. Anal. Math. 75 (1998), 267-297.

Bo1999 J. Bourgain, New global well-posedness results for non-linear Schrodinger equations, AMS 1999.

Bo1999b J. Bourgain, Global well-posedness of defocussing 3D critical NLS in the radial case, J. Amer. Math. Soc. 12 (1999), 145-171.

Bo-p J. Bourgain, Remarks on stability and diffusion in high-dimensional Hamiltonian systems and PDE, preprint.

Bo-p2 J. Bourgain, A remark on normal forms and the I-method for periodic NLS, preprint.

Bo-p3 J. Bourgain, On the Cauchy problem for periodic KdV type equations, preprint.

BoCo1996 J. Bourgain, J. Colliander, On the well-posedness of the Zakharov system, IMRN 11 (1996), 515-546.

BoWg1997 J. Bourgain, W. Wang, Construction of blowup solutions for the nonlinear Schrodinger equation with critical non-linearity, Dedicated to Ennio De Giorgi. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997), no. 1-2, 197-215.

Bou1996 N. Bournaveas, Local existence for the Maxwell-Dirac equations in three space dimensions. Comm. Partial Differential Equations 21 (1996) 693-720.

Bou1999 N. Bournaveas, Local existence of energy class solutions for the Dirac-Klein-Gordon equations. Comm. Partial Differential Equations 24 (1999), 1167-1193.

Bou2000 N. Bournaveas, A new proof of global existence for the Dirac Klein-Gordon equations in one space dimension. J. Funct. Anal. 173 (2000), 203-213.

Bou2001 N. Bournaveas, Low regularity solutions of the Dirac Klein-Gordon equations in two space dimensions. Comm. Partial Differential Equations 26 (2001), 1345-1366.

BdmFsShp-p A. Boutet de Monvel, A. Fokas, The mKdV equation on a half-line, preprint.

BdmShp-p A. Boutet de Monvel, D. Shepelsky, The mKdV equation on an interval, preprint.

BrlForMai1994 P. Breitenlohner, P. Forgacs, D. Maison, Static spherically symmetric solutions of the Einstein-Yang-Mills equations. Comm. Math. Phys. 163 (1994), no. 1, 141-172.

Br1975 P. Brenner, On L^p - L^{p'} estimates for the wave equation, Math Z. 145 (1975) 251-254.

Br1984 P. Brenner, On spacetime means and everywhere defined scattering operators, Math. Z. 186 (1984), 383-391.

Br1985 P. Brenner, On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations, JDE 56 (1985), 310-344.

BrKum2000 P. Brenner, P. Kumlin, On wave equations with supercritical nonlinearities, Arch. Math. 74 (2000), 129-147.

BrzGa1980 H. Brezis, T. Gallouet, Nonlinear Schrodinger evolution equations, Nonlinear Analysis Theory, Methods, and Applications 4 (1980), 677-681.

Bs1967 A.R. Brodsky, On the asymptotic behaviour of solutions of the wave equation, Proc. Amer. Math. Soc. 18 (1967), 207-208.

BroJer2000 J. Bronski, R. Jerrard, Soliton dynamics in a potential, Math Res. Lett. 7 (2000), 329-342.

Bu.1992 C. Bu, On the Well-Posedness of the forced nonlinear Schrodinger Equation, Appl. Anal. 46 (1992), 219-239.

Bu.2000 C. Bu, Nonlinear Schrodinger Equation on the Semi-infinite Line, Chinese J. Contem. Math. 21 (2000), 209-222

Bu.Sr2001 C. Bu, W. Strauss, An inhomogeneous Boundary Value Problem for Nonlinear Schrodinger Equations, JDE 173 (2001), 79-91.

Bub1980 B. Bubnov, On the Cauchy problem for the Korteweg de Vries equation, Soviet Math. Dokl. 21 (1980), 502-505.

Bu1998 N. Burq, Decroissance de l'energie locale de l'equation des ondes pour les probleme exterieur et absece de resonance au voisinage du reel, Acta Math. 180 (1998), 1-29.

Bu1993 N. Burq, Controle l'equation des plaques en presence d'obstacles strictement convexes, Memorie de la SMF 55 (1993), Suppl. au Belletin de la Societe Mathematique de France.

Bu-p2 N. Burq, Smoothing effect for Schrodinger boundary value problems, preprint.

Bu-p3 N. Burq, Estimations de Strichartz pour des perturbations a longe portee de l\u2019operateur de Schrodinger, preprint.

BuGdTz-p N. Burq, P. Gerard, N. Tzvetkov, Two singular dynamics of the nonlinear Schrodinger equation on a plane domain, preprint.

BuGdTz2002 N. Burq, P. Gerard, N. Tzvetkov, An instability property of the nonlinear Schrodinger equation on S^d, MRL 9 (2002), 323-335.

BuGdTz-p3 N. Burq, P. Gerard, N. Tzvetkov, Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds, preprint.

BuGdTz-p4 N. Burq, P. Gerard, N. Tzvetkov, On nonlinear Schrodinger equations in exterior domains, preprint.

BuGdTz2003 N. Burq, P. Gerard, N. Tzvetkov, The Cauchy problem for the nonlinear Schrodinger equation on a compact manifold, Proc. Oresund Symposium on PDE, Lund, May 2002, J. Nonlinear Math. Phys. 10 suppl 1. (2003), 1-16.

BuGdTz-p6 N. Burq, P. Gerard, N. Tzvetkov, An example of singular dynamics for the nonlinear Schrodinger equation on bounded domains, Proc. conference on hyperbolic PDE and related topics, Cortona September 2002, preprint.

BuGdTz-p7 N. Burq, P. Gerard, N. Tzvetkov, Bilinear Eigenfunction Estimates and the Nonlinear Schroedinger Equation on Surfaces, preprint.

BuPlStaTv-p N. Burq, F. Planchon, J. Stalker, A. Shadi Tahvidar-Zadeh, Strichartz estimates for the Wave and Schrodinger Equations with the Inverse-Square Potential, preprint.

BuPlStaTv-p2 N. Burq, F. Planchon, J. Stalker, A. Shadi Tahvidar-Zadeh, Strichartz estimates for the Wave and Schrodinger Equations with potentials of critical decay, preprint.

BusPer1993 V. Buslaev, G. Perelman, Scattering for the nonlinear Schrodinger equations: states close to a solitary wave, St. Petersburg Math J. 4 (1993), 1111-1142.

BusPer1995 V. Buslaev, G. Perelman, On the stability of solitary waves for nonlinear Schrodinger equations.Nonlinear evolution equations 75-98, Amer. Math. Soc. Transl. Ser. 2, 164, Amer. Math. Soc. Providence, RI 1995.

BusSuc2003 V. Buslaev, C. Sulem, On asymptotic stability of solitary waves for nonlinear Schrodinger equations, Ann. Inst. H. Poincare Anal. Nonlineaire 20 (2003) 3, 419-475.

C

CafFri1986 L.A. Caffarelli, A. Friedman, the blowup boundary for nonlinearwave equations, TAMS 297 (1986), 223-241.

Cal-p S. Calogero, Global small solutions of the Vlasov-Maxwell system in absence of incoming radiation., preprint

Car2001 R. Carles, Geometric optics and long-range scattering for one-dimensional nonlinear Schrodinger equations, Comm. Math. Phys. 220 (2001), 41-67.

Car2002 R. Carles, Critical nonlinear Schrodinger equations with and without harmonic potential, Math. Mod. Meth. Appl Sci. 12 (2002), 1513-1523..

Car2002b R. Carles, Remarks on nonlinear Schrodinger equations with harmonic potential, Ann. Henri Poincare 3 (2002), 757-772.

Car2002c R. Carles, Critical nonlinear Schrödinger equations with and without harmonic potential, Math. Mod. Meth. Appl. Sci. (M3AS) 12 (2002), 1513-1523

Car2003 R. Carles, Annales IHP, Analyse nonlineaire, 20 (2003) 501-542.

CarFerGal-p R. Carles, C. Fermanian, I. Gallagher, On the role of quadratic oscillations in nonlinear Schrodinger equations, preprint.

CarKer-p R. Carles, S. Keraani, On the role of quadratic oscillations in nonlinear Schroedinger equations II. The $L^2$-critical case, preprint.

CarNky-p R. Carles, Y. Nakamura, Nonlinear Schrodinger equations with Stark potential, preprint.

CarRa-p R. Carles, J. Rauch, Focusing of spherical nonlinear pulses in R^{1+3} III. Sub and supercritical cases, preprint.

CrrBu1991 R. Carrol, C. Bu, Solution of the Forced Nonlinear Schrodinger Equation (NLS) Using PDE Techniques, Appl. Anal. 41 (1991), 31-51.

Cv2002 X. Carvajal, Propriedades das solucoes de uma equacao de Scrodinger nao linear de alta ordem, PhD Thesis, Instituto de matematica pura e aplicada, IMPA, Rio de Janeiro, Brazil, (2002).

Cv2004 X. Carvajal, Local well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices , Electron. J. Diff. Eqns., Vol. 2004(2004), No. 13, pp. 1-10.

CvLi2003 X. Carvajal, F. Linares, A higher order nonlinear Schr\"odinger equation with variable coefficients, Differential and Integral Equations, 16, 9, (2003), 1111\u20141130.

CvLi-p X. Carvajal, F. Linares, Some properties for a higher order nonlinear Schr\"odinger equation, Preprint.

CvPan-p X. Carvajal, M. Panthee, Unique continuation property for a higher

• oder nonlinear Schr\"odinger equation, Preprint.

Ca1985 T. Cazenave, Uniform estimates for solutions of non-linear Klein-Gordon equations, J. Func. Anal. 60 (1985), 36-55.

Ca1989 T. Cazenave, An introduction to nonlinear Schrodinger equations, Textos de Metodes Matematicos 22 (Rio de Janeiro), 1989.

Ca1994 T. Cazenave, Blow up and scattering in the nonlinear Schrodinger equation, Textos de Metodes Mathematicos 30 (Rio de Janeiro), 1994.

CaHz1990 T. Cazenave, A. Haraux, Introduction aux problemes d'evolution semi-lineaires, SMAI, Ellipses (1990)

CaLo1982 T. Cazenave, P. Lions, Orbital stability of standing waves for some nonlinear Schrodinger equations, Comm. Math. Phys. 68 (1979), 209-243.

CaWe1990 T. Cazenave, F.B. Weissler, The Cauchy problem for the critical nonlinear Schrodinger equation, Non. Anal. TMA, 14 (1990), 807-836.

CaWe1992 T. Cazenave, F.B. Weissler, Rapidly decaying solutions of the nonlinear Schrodinger equation, Comm. Math. Phys. 47 (1992), 75-100.

CaWe1998 T. Cazenave, F.B. Weissler, Asymptotically self-similar global solutions of the nonlinear Schrodinger and heat equations, Math. Z. 228 (1998), 83-120.

CaWe1998b T. Cazenave, F.B. Weissler, More self-similar global solutions of the nonlinear Schrodinger equation, Nonlinear Diff. Eq. Appl. 5 (1998), 355-365.

CaSaTv1998 T. Cazenave, J. Shatah, A.S. Tahvildar-Zadeh, Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields, Ann. Inst. H. Poincaré Phys. Théor.68 (1998), 315-349.

CaVeVi-p T. Cazenave, L. Vega, M.C. Vilela, A note on the nonlinear Schrodinger equation in weak L^p spaces, preprint.

Chd1973 J.M. Chadam, Global solutions of the Cauchy problem for the (classical) Maxwell-Dirac equations in one space dimension, J. Funct. Anal 13. (1973), 173 - 184.

CgSaUh2000 N. Chang, J. Shatah, K. Uhlenbeck, Schrodinger maps, CPAM 52 (2000), 590-602

Ch2000 J.Y. Chemin, Explosion geometrique pour certaines equations d\u2019ondes nonlineaires [d\u2019apres Serge Alinhac], Seminaire Bourbaki Exp. 850, Asterique 266 (2000), 7-20.

Ci1994 H. Chihara, Local existence for the semilinear Schrodinger equations in one space dimension, J. Math. Kyoto Univ. 34 (1994), 353-367.

Ci1995 H. Chihara, Local existence for semilinar Schrodinger equations, Math. Japon. 42 (1995), 35-52.

Ci1996 H. Chihara, The initial value problem for cubic semilinear Schrodinger equations, Publ. Res. Inst. Math. Sci. 32 (1996), 445-471.

Ci1999 H. Chihara, Gain of regularity for semilinear Schrodinger equations, Math. Ann. 315 (1999), 529-567.

Ci2002 H. Chihara, The initial value problem for Schrodinger equations on the torus, IMRN 15 (2002), 789-820.

Ci-p H. Chihara, Third order semilinear dispersive equations related to deep water waves, preprint.

Chp1993 M.W. Choptuik, Phys. Rev. Lett. 70 (1993), 9

Cq1952 Y. Choquet-Bruhat, Theorem d\u2019Existence pour certains sytemes d\u2019equations aux derivees partielles nonlineaires, Acta Math 88 (1952), 141-225

Cq1973 Y. Choquet-Bruhat, Un theoreme d\u2019instabilit pour certains equations hyperboliques nonlineaires, C.R. Acad. Paris Sr. A-B 276 (1973), A281-A284.

Cq1987 Y. Choquet-Bruhat, Global existence theorems for hyperbolic harmonic maps, Ann. Inst. H. Poincare Phys. Theor. 46 (1987), 97-111.

Cq2000 Y. Choquet-Bruhat, The null condition and asymptotic expansions for Einstein\u2019s equations, Ann. Phys. (Leipzig) 9 (2000), 258-266.

Cq-p Y. Choquet-Bruhat, Wave maps in general relativity, preprint.

Cq-p2 Global wave maps on curved space times, preprint.

CqCd1981 Y. Choquet-Bruhat, D. Christodoulou, Existence of global solutions of the Yang-Mills, Higgs, and spinor field equations in 3+1 dimensions, Ann. Sci. Ecole Norm. Sup. (4) 14 (1981), 481-506.

CqGc1969 Y. Choquet-Bruhat, R. Geroch, Global aspects of the Cauchy problem in General Relativity, CMP 14 (1969), 329-335.

CtCoTa-p M. Christ, J. Colliander, T. Tao, Asymptotics, frequency modulation, and low-regularity illposedness of canonical defocussing equations, preprint.

CtCoTa-p2 M. Christ, J. Colliander, T. Tao, Low-regularity ill-posedness for nonlinear Schrodinger and wave equations, preprint.

CtCoTa-p3 M. Christ, J. Colliander, T. Tao, Instability of the periodic nonlinear Schrodinger equation, preprint.

CtWs1991 M. Christ, M. Weinstein, Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal. 100 (1991), 87-109.

Cd1981 D. Christodoulou, Solutions globales des equations de champ de Yang-Mills, C. R. Acad. Sci. Paris Series A 289 (1981), 481-506.

Cd1986 D. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math, 39 (1986), 267-282.

CdKl1990 D. Christodoulou, S. Klainerman, Asymptotic properties of linear field equations in Minkowski space, Comm. Pure Appl. Math, (1990), 137-199

CdKl1993 D. Christodoulou, S. Klainerman, The global nonlinear stability of the Minkowski space, Princeton Mathematical Series 41 (1993)

CdTv1993 D. Christodoulou, A. Tahvildar-Zadeh, On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math, 46 (1993), 1041-1091.

CdTv1993b D. Christodoulou, A. Tahvildar-Zadeh, On the asymptotic behavior of a spherically symmetric wave map, Duke Math. J. 71 (1993), 31-69.

CcSa1997 P. Chrusciel, J. Shatah, Global existence of solutions of the Yang-Mills equations on globally hyperbolic four-dimensional Lorentzian manifolds Asian J. Math. 1 (1997), no. 3, 530-548.

Coh1992 S. Cohn, Resonance and long time existence for the quadratic nonlinear Schrodinger equation, CPAM 45 (1992), 973-1001.

Coh1994 S. Cohn, Global existence for the nonresonant Schrodinger equation in two space dimensions, Canad. Appl. Math. Quart. 2 (1994), 257-282.

CoiWic1990 R. Coifman, V. Wickerhauser, The scattering transform for the Benjamin-Ono equation, Inverse Problems (1990) 6, 825-861.

Cn1993 T. Colin, Effects regularisants pour des equations dispersive obtenus par une transformee de Wigner generalisee, C. R. Acad. Sci. Paris, Ser. I. Math 317 (1993), 673-676.

Col2002 M. Colin, On the local well-posedness of quasilinear Schrodinger equations in arbitrary space dimension, CPDE 27 (2002), 325-354.

Col2003 M. Colin, Stability of stationary waves for a quasilinear Schrödinger equation in space dimension 2. Adv. Differential Equations 8 (2003), no. 1, 1--28.

Co1996 J. Colliander, Globalizing estimates for the KP-I equation, Illinois J. Math. 40 (1996), 692-698.

Co1997 J. Colliander, The initial value problem for the Zakharov system, PhD Thesis, U. Illinois, 1997.

CoKeStTkTa2001 J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Global well-posedness for KdV in Sobolev spaces of negative index, EJDE 2001 (2001) No 26, 1-7.

CoKeStTkTa2001b J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Global well-posedness for the Schrodinger equations with derivative, SIAM J. Math. Anal. 33 (2001), 649-669.

CoKeStTkTa2002 J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Almost conservation laws and global rough solutions to a nonlinear Schrodinger equation, Math Res. Lett. 9 (2002), 5-6, 659-682.

CoKeStTkTa2002b J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, A refined global well-posedness for the Schrodinger equations with derivative, SIAM J. Math. Anal. 34 (2002), 64-86.

CoKeStTkTa2003 J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, [math.AP/0110045 Sharp global well-posedness results for periodic and non-periodic KdV and modified KdV on R and T], JAMS 16 (2003), 705-749.

CoKeStTkTa2003b J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm, Discrete Contin. Dyn. Syst. 9 (2003), 31-54.

CoKeStTkTa2003c J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Polynomial growth and orbital instability bounds for $L^2$-subcritical NLS below the energy norm, Commun. Pure Appl. 2 (2003), 33-50.

CoKeStTkTa-p J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Global well-posedness and scattering in the energy space for the critical nonlinear Schrodinger equation in R^3, preprint

CoKeStTkTa-p3 J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Multi-linear estimates for periodic KdV equations, and applications, preprint

CoKeStTkTa-p5 J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Further global well-posedness results for 2D NLS, preprint.

CoKeStTkTa-p8 J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Scattering for cubic 3D NLS below the energy norm, preprint.

CoKeStTkTa-p9 J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Symplectic non-squeezing for periodic KdV, preprint

CoKn-p J. Colliander, C. Kenig, The generalized Korteweg-de Vries equation on the half line, preprint

CoKnSt-p J. Colliander, C. Kenig, G. Staffilani, Local well-posedness and regularity properties of solutions of the generalized Kadomtsev-Petviashvili equations, preprint.

CoKnSt-p2 J. Colliander, C. Kenig, G. Staffilani, Low regularity solutions of the Kadomtsev-Petviashvili-I equation, preprint.

CoKnSt-p3 J. Colliander, C. Kenig, G. Staffilani, Small solutions for the Kadomtsev-Petviashvili I equation, Mosc. Math J. 1 (2001), 491-520.

CoKnSt-p4 J. Colliander, C. Kenig, G. Staffilani, Local well-posedness for dispersion generalized Benjamin-Ono equations, preprint.

CoSt-p J. Colliander, G. Staffilani, Regularity bounds on Zakharov System evolutions, EJDE 2002 (2002) No 75, 1-11.

ConSau1988 P. Constantin, J.C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988), 413-439.

ConSau1989 P. Constantin, J.C. Saut, Local smoothing properties of Schrodinger equations, Indiana U. Math. J. 38 (1989), 781-810.

CkGr-p G. Costakis, M. Grillakis, Local and global existence for the Schrodinger map problem, preprint

CrKpSr1992 W. Craig, T. Kappeler, W. Strauss, Gain of regularity for equations of the Korteweg-de Vries type, Ann. Inst. Henri Poincare 9 (1992), 147-186.

CrKpSr1995 W. Craig, T. Kappeler, W. Strauss, Microlocal dispersive smoothing for the Schrodinger equation, Comm. Pure Appl. Math 48 (1995), 769-860.

Cs1980 C. Cronstrom, A simple and complete Lorentz-invariant gauge condition, Phys. Lett. B 90 (1980), 267-269.

Cu1999 S. Cuccagna, On the local existence for the Maxwell-Klein-Gordon system in R^{3+1}, Comm. Partial Differential Equations. 24 (1999), 851-867.

Cu2001 S. Cuccagna, Stabilization of solutions to nonlinear Schrodinger equations, CPAM 54 (2001), 1110-1145.

Cu2001 S. Cuccagna, On asymptotic stability of ground states of NLS, preprint.

D

DanGe-p P. D'Ancona, V. Georgiev, On the continuity of the solution operator of the wave maps system, preprint

DanPie-p P. D\u2019Ancona, V. Pierfelice, On the wave equation with large rough potential, preprint.

DaKn1982 B. Dahlberg, C. E. Kenig, A note on the almost everywhere behaviour of solutions to the Schrodinger equation, Harmonic Analysis, Lecture Notes in Math., Springer Verlag, 908, (1982), 205-208.

Dt1990 P. Datti, Nonlinear wave equations in exterior domains, Nonlinear Anal. 15 (1990), 321-331.

DavSte1974 A. Davey, K. Stewartson, On three dimensional packets of surface waves, Proc. R. Soc. A 338 (1974), 101-110.

DbDM2002 A. Debussche, L. Di Menza, Numerical simulation of the nonlinear stochastic Schrodinger equation, Phys D 162 (2002), 131-154.

DfZx1994 P. Deift, X. Zhou, Long-time asymptotics for integrable systems. Higher order theory, Comm. Math. Phys. 165 (1994), 175-191.

De1997 J. Delort, Sur le temps d'existence pour l'equation de Klein-Gordon semi-lineaire en dimension 1, Bull. Soc. Math. France 125 (1997), 269-311.

De1997b J. Delort, L'équation de Klein-Gordon à données petites faiblement décroissantes, Séminaire sur les Équations aux Dérivées Partielles, 1996-1997, Exp. No. V, 14 pp., École Polytech., Palaiseau, 1997.

De1998 J. Delort, Temps d'existence pour l'équation de Klein-Gordon semi-linéaire à données petites périodiques, Amer. J. Math. 120 (1998), 663-689.

De1999 J. Delort, Minoration du temps d'existence pour l'équation de Klein-Gordon non-linéaire en dimension 1 d'espace, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), 563-591.

De2001 J. Delort, Existence global et comportement asymptotique pour l'equation de Klein-Gorodn quasi lineaire a donnees petites en dimension 1, Ann. Sci. Ecole Norm. Sup. 34 (2001), 1-61.

De2002 J. Delort, Global solutions for small nonlinear long-range perturbations of two-dimensional Schrodinger equations, Societe Mathematique de France.

DeFg-p J. Delort, D. Fang, Almost global existence of solutions of semilinear Klein-Gordon equations with small weakly decaying Cauchy data, CPDE to appear.

DeFgXue-p J. Delort, D. Fang, R. Xue, Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions, preprint.

DeSze-p J. Delort, J. Szeftel, Long time existence for small data nonlinear Klein-Gordon equations on tori and spheres, IMRN 2004:37 (2004) 1897-1966

DiaFi1989 J. Dias, M. Figueira, On the existence of weak solutions for a time-dependent nonlinear Dirac equation, Proc. Royal Soc. Edinburgh 113A (1989), 149-158.

Di1998 Q. Ding, A note on the NLS and the Schrodinger flow of maps, Phys. Lett A. 248 (1998) 49-56.

Di1999 Q. Ding, The gauge equivalence of the NLS and the Schrodinger flow of maps in 2+1 dimensions, J. Phys. Math. A.; Math. Gen. 32 (1999), 5087-5096.

Di-p Q. Ding, On Schrodinger flows to the Hyperbolic 2-space, preprint.

Di2002 W. Ding, On the Schrodinger flows, Proc. ICM Beijing 2002, vol 2, 283-292.

DiWgy1998 W. Ding, Y. Wang, Schrodinger flow of maps into symplectic manifolds, Science in China (Series A) 41 (1998), 746-755.

DiWgy2001 W. Ding, Y. Wang, Local Schrodinger flow into Kahler manifolds. Science in China (Series A) 44 (2001), 1446-1464.

Do1994 S. Doi, On the Cauchy problem for Schrodinger type equations and the regularity of the solutions, J. Math. Kyoto U. 34 (1994), 319-328.

Do1996 S. Doi, Remarks on the Cauchy problem for Schrodinger type equations, CPDE 21 (1996), 163-178.

Do2000 S. Doi, Smoothing effects for Schrodinger evolution equation and global behavior of geodesic flow, Math Ann. 318 (2000), 355-389.

Do-p S. Doi, On the regularity of solutions for some semilinear Schrodinger equations, preprint.

DonLs1981 G.C. Dong, S.J. Li, On the initial value problem for a nonlinear Schrodinger equation, JDE 42 (1981) 353-365.

Du1982 O. Dumitrascu, Equivariant solutions of the Yang-Mills equations. (Romanian. English summary) Stud. Cerc. Mat. 34 (1982), 329-333.

Duy-p T. Duyckaerts, A singular critical potential for the Schrodinger operator, preprint.

Dy1979 K.B. Dysthe, Note on a modification to the nonlinear Schrodinger equation for application to deep water, Proc. Roy. Soc. London Ser. A. 369 (1979), 105\u2014114.

E

EaMc1982 D. Eardley, V. Moncrief, The global existence of Yang-Mills-Higgs fields in R^{3+1}, Comm. Math. Phys. 83 (1982), 171-212.

EckShr1983 W. Eckhaus, P. Schuur, The emergence of solutions to the Korteweg-de Vries equation from arbitrary initial conditions, Math Meth. Appl. Sci. 5 (1983), 97-116.

El2003 K. El Dika, Stabilite asymptotique des ondes solitaires de l\u2019equation de Benjamin-Bona-Mahony, C. R. Acad. Sci. Paris Ser. I 337 (2003), 649\u2014652.

El-p K. El Dika, Asymptotic stability of solitary waves for the Benjamin-Bona-Mahony equation, Preprint 2003.

EscVe1997 M. Escobedo, L. Vega, A semilinear Dirac equation in H^s(R^3) for s > 1, Siam J. Math Anal. 28 (1997), 338-362.

EsSer2002 M. Esteban, E. Sere, An overview of linear and nonlinear Dirac equations, Discrete Cont. Dynamical Systems 8 (2002), 381-397.

EsSr1994 M. Esteban, W. Strauss, Nonlinear bound states outside an insulated sphere, CPDE 19 (1994), 177-194.

F

FgGl1996 Y. Fang, M. Grillakis, A priori estimates for the 2-D wave equation. Comm. Partial Differential Equations 21 (1996), no. 9-10, 1643-1665.

Fa1983 A. Faminskii, The Cauchy problem and the mixed problem in the half strip for equations of Korteweg-de Vries type (Russian), Dinamika Sploshn. Sredy 162 (1983), 152-158.

Fa1990 A.V. Faminski, The Cauchy problem for the Kadomtsev-Petviashvili equation, Russian Math. Sur. 5 (1990), 203-204.

FerMeZaa2000 C. Fermanian, F. Merle, H. Zaag, Stability of the blowup profile of a nonlinear heat equations from dynamical systems point of view, Math. Ann. 317 (2000), 347-387.

FtSnTl1987 M. Flato, J. Simon, E. Taflin, On global solutions of the Maxwell-Dirac equations, CMP 112 (1987), 21-49.

Fo-p G. Fonseca, Global well-posedness for two dimensional semilinear wave equations, preprint.

FoLiPo1999 G. Fonseca, F. Linares, G. Ponce, Global well-posedness for the modified Korteweg-de Vries equation, Comm. Partial Differential Equations. 24 (1999), 683-705.

FoLiPo-p G. Fonseca, F. Linares, G. Ponce, Global well-posedness for the critical generalized KdV equation, preprint.

Fs2002 A.S. Fokas, Integrable nonlinear evolution equations on the half-line, CMP 230 (2002), 1-39.

FsAb1984 A.S. Fokas, M. Ablowitz, The inverse scattering transform for the Benjamin-Ono equation: a pivot to multidimensional problems, Stud. Appl. Math. (1984) 68, 1-10.

FsIt-p A.S. Fokas, A.R. Its, The nonlinear Schrodinger equation on an interval, preprint.

FsLu2000 A.S. Fokas, L. Luo, Global solutions and their asymptotic behavior for Benjamin-Ono-Burgers type equations, DIE 13 (2000), 115-124.

FsSng1992 A.S. Fokas, L. Y. Sung, On the solvability of the N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations, Inverse Problems 8 (1992), 673-708.

Fc2000 D. Foschi, On the regularity of multilinear forms associated to the wave equation, PhD Thesis, January 2000.

Fc2000b D. Foschi, On an endpoint case of the Klainerman-Machedon estimates, CPDE 25 (2000), 1537-1547.

Fc-p D. Foschi, Proof of a conjecture on trilinear estimates, preprint 1999.

Fc-p2 D. Foschi, Inhomogeneous Strichartz estimates, preprint.

Fc-p3 D. Foschi, Some remarks on the L^p \u2013 L^q boundedness of trigonometric sums and oscillatory integrals, preprint.

Fc-p4 D. Foschi, Maximizers for the Strichartz inequality, preprint.

FrMuSw1998 A. Freire, S. Muller, M. Struwe, Weak compactness of wave maps and harmonic maps, Ann. IHP. Anal. Nonlineaire 15 (1998), 725-754.

FroTsaYau2002 J. Frohlich, T. Tsai, H. Yau, On the point-particle (Newtonian) limit of the non-linear Hartree equation, CMP 225 (2002), 223-274.

Fuj1979 D. Fujiwara, A construction of the fundamental solution for the Schrodinger equation, J. Analyse Math. 35 (1979), 41-96.

Fuj1980 D. Fujiwara, Remarks on the convergence of the Feynman path integrals, Duke Math J. 47 (1980), 559-600.

FuTs1978 I. Fukuda, Y. Tsutsumi, On coupled Klein-Gordon-Schrodinger equations II, J. Math. Anal. Appl. 66 (1978), 358-378.

FuTs1980 I. Fukuda, Y. Tsutsumi, On solutions of the derivative nonlinear Schrodinger equation: existence and uniqueness theorem, Funkcial. Ekvac. 23 (1980), 259-277.

FuTs1981 I. Fukuda, Y. Tsutsumi, On solutions of the derivative nonlinear Schrodinger equation II, Funkcial. Ekvac. 234 (1981), 85-94.

Fuk2001 R. Fukuizumi, Stability and instability of standing waves for the nonlinear Schr\"odinger equation with harmonic potential, Discrete Contin. Dynam. Systems. 7 No.3 (2001) pp. 525-544

Fuk2003 R. Fukuizumi, Remarks on the stable standing waves for nonlinear Schr\"odinger equations with double power nonlinearity, to appear in Advances in Mathematical Sciences and Applications. 13 No. 2 (2003)

FukOt2003 R. Fukuizumi, M. Ohta, Instability of standing waves for nonlinear Schr\"odinger equations with potentials, Differential and Integral Equations. vol.16 No.6 (2003) pp. 691-706.

FukOt2003b R. Fukuizumi, M. Ohta, Stability of standing waves for nonlinear Schr\"odinger equations with potentials, Differential and Integral Equations. Vol.16 No.1 (2003) pp. 111-128

Fur2001 G. Furioli, On the existence of self-similar solutions of the nonlinear Schrodinger equation with power nonlinearity between 1 and 2, DIE 14 (2001), 1259-1266.

FurPlTer2001 G. Furioli, F. Planchon, E. Terraneo, Unconditional well-posedness for semilinear Schrodinger and wave equations in H^s, Harmonic Analysis at Mount Holyoke (2001), 367-382, W. Beckner, A. Nagel, A. Seeger, H. Smith editors, AMS.

FurTer-p G. Furioli, E. Terraneo, Besov spaces and unconditional well-posedness for the semilinear Schrodinger in H^s, preprint.

G

GalGd2001 I. Gallagher, P. Gerard, Profile decomposition for the wave equation outside a convex obstacle, JMPA 80 (2001), 1-49.

GalPl2003 I. Gallagher, F. Planchon, On global solutions to a defocusing semi-linear wave equation, Rev. Mat. Iberoamericana 19 (2003), 161-177.

GarGreKruMi1967 C. Gardner, J. Greene, M. Kruskal, R. Miura, A method for solving the Korteweg-de Vries equation, Phys. Rev. Letters 19 (1967), 1095-1097.

GarGreKruMi1974 C. Gardner, J. Greene, M. Kruskal, R. Miura, The Korteweg-de Vries equation and its generalizations VI, Method for exact solutions, CPAM 27 (1974), 87-133.

GeaGw1984 J. A. Gear, R. Grimshaw, Weak and strong interactions between internal solitary waves, Stud. Appl. Math. 65 (1984), 235-258.

Gd1992 P. Gerard, Remarques sur l'analyse semi-classique de l'equation Schrodinger non lineaire, Seminaire EDP de l'Ecole Polytechnique (1992), lecture XIII.

Ge1991 V. Georgiev, Small amplitude solutions of the Maxwell-Dirac equations, IUMJ 40 (1991), 845-883.

GeIv-p V. Georgiev, A. Ivanov, Concentration of local energy for two dimensional wave maps, preprint.

GeLbSo1997 V. Georgiev, H. Lindblad, C. Sogge, Weighted Strichartz estimates and global existence for semilinear wave equations, Am. J. Math. 119 (1997) 1291-1319.

GePp1991 V. Georgiev, P. Popivanov, Global solution to the two-dimensional Klein-Gordon equation, CPDE 16 (1991), 941-995.

GeVis2003 V. Georgiev, N. Visciglia, Decay estimate for the wave equation with potential, CPDE 28 (2003), 1325-1369.

GhSau1990 J.M. Ghidaglia, J.C. Saut, On the initial value problem for the Davey-Stewartson system, Nonlinearity 3 (1990), 475-506

GhSau1992 J.M. Ghidaglia, J.C. Saut, On the Zakharov-Schulman equations, Nonlinear Dispersive Waves, L. Debnath ed. World Scientific (1992),

Gi1994 J. Ginibre, Scattering theory in the energy space for a class of nonlinear wave equations, "Spectral and Scattering Theory and Application", Adv. Stud. Pure. Math. 23 Kinokuniya Toyko (1994), 83-103.

Gi1994b J. Ginibre, Equations d'Evolution Semilinearies: L'Equation de Schrodinger Non-lineaire, Cours de DEA, Universite de Paris-Sud, Paris 1994

Gi1995 J. Ginibre, An introduction to nonlinear Schrödinger equations. Hokkaido University Technical Report Series in Mathematics 43 (1996) 80-128.

Gi1998 J. Ginibre, Le probléme de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace (d'aprés Bourgain), Séminaire Bourbaki 1994/1995, Asterisque 237 (1996), Exp. 796, 163-187.

GiOz1993 J. Ginibre, T. Ozawa, Long range scattering for nonlinear Schrodinger and Hartree equations in space dimension n>=2, CMP 151 (1993) 619-645.

GiOzVl1994 J. Ginibre, T. Ozawa, G. Velo, On the existence of the wave operators for a class of nonlinear Schrodinger equations, Ann. Inst. H. Poincare Pys. Theor. 60 (1994), 211-239.

GiSfVl1992 J. Ginibre, A. Soffer, G. Velo, The global Cauchy problem for the critical non-linear wave equation, J. Funct. Anal. 110 (1982), 96-130.

GiTs1989 J. Ginibre, Y. Tsutsumi, Uniqueness for the generalized Korteweg-de Vries equations, SIAM J. Math. Anal. 20 (1989), 1388-1425.

GiTsVl1990 J. Ginibre, Y. Tsutsumi, G. Velo, Existence and uniqueness of solutions for the generalized Korteweg de Vries equation, Math. Z. 203 (1990), 9-36.

GiTsVl1997 J. Ginibre, Y. Tsutsumi, G. Velo, On the Cauchy problem for the Zakharov system, J. Funct. Anal. 151, (1997) 384-436.

GiVl1978 J. Ginibre, G. Velo, Scattering theory in the energy space for a class of nonlinear Schrodinger equations, J. Math. Pures Appl. 64 (1985), 363-401.

GiVl1979 J. Ginibre, G. Velo, On a class of nonlinear Schrodinger equations, J. Funct. Anal. 32 (1979), 1-71.

GiVl1980 J. Ginibre, G. Velo, On a class of nonlinear Schrodinger equations with nonlocal interactions, Math Z. 170 (1980), 109-136.

GiVl1982 J. Ginibre, G. Velo, The Cauchy problem for the O(N), CP(N-1), and GC(N,P) models, Ann. Physics, 142 (1982), 393-415.

GiVl1982b J. Ginibre, G. Velo, The Cauchy problem for coupled Yang-Mills and scalar fields in the temporal gauge, CMP 82 (1981/1982), 1-28.

GiVl1985 J. Ginibre, G. Velo, Scattering Theory in the Energy Space for a Class of Nonlinear Schrodinger Equations, J. Math. Pure Appl., 64 (1985), 363-401.

GiVl1985b J. Ginibre and G. Velo, Time decay of finite energy solutions of the non linear Klein-Gordon and Schr\"odinger equations, Ann. Inst. Henri. Poincar\'e, 43 (1985), 399-442.

GiVl1985c J. Ginibre, G. Velo, The global Cauchy problem for the non linear Klein-Gordon equation, Math. Z. 189 (1985), 487-505.

GiVl1985d J. Ginibre, G. Velo, The global Cauchy problem for the nonlinear Schrodinger equation revisited, Annales I.H.P., Analyse non lineaire 2 (1985), 309-327.

GiVl1987 J. Ginibre, G. Velo, Conformal invariance and time decay for nonlinear wave equations I. Ann. Inst. Henri Poncare Phys. Theor. 47 (1987), 221-261.

GiVl1987b J. Ginibre, G. Velo, Conformal invariance and time decay for nonlinear wave equations II. Ann. Inst. Henri Poncare Phys. Theor. 47 (1987), 263-276.

GiVl1989 J. Ginibre, G. Velo, Scattering theory in the energy space for a class of non-linear wave equations, Comm. Math. Phys., 123 (1989), 535-573.

GiVl1989b J. Ginibre, G. Velo, Proprietes de lissage et existence de solutions pour l'equation de Benjamin-Ono generalisee, C.R. Acad. Sci. Paris 308 (1989), 309-314.

GiVl1991 J. Ginibre, G. Velo, Smoothing properties and existence of solutions for the generalized Bejamin-Ono equations, JDE 93 (1991), 150-232.

GiVl1992 J. Ginibre, G. Velo, Smoothing properties and retarded estimates for some dispersive evolution equations, Comm. Math. Phys. 144 (1992), 163-188.

GiVl1995 J. Ginibre, G. Velo, Generalized Strichartz Inequalities for the Wave Equation, J. Func. Anal., 133 (1995), 50-68.

GiVl1995b J. Ginibre, G. Velo, Le probleme de Cauchy pour des EDP semi-lineaires periodiques en variables d'espace (d'apres Bourgain), Seminaire Bourbaki 796, Asterisque 237 (1985), 163-187.

GiVl2000 J. Ginibre, G. Velo, Long range scattering and modified wave operators for some Hartree type equations I, Rev. Math. Phys. 12 (2000), 361-429.

GiVl2000b J. Ginibre, G. Velo, Long range scattering and modified wave operators for some Hartree type equations II, Ann. Henri Poincare 1 (2000), 753-800.

GiVl2001 J. Ginibre, G. Velo, Long range scattering and modified wave operators for some Hartree type equations III, J. Diff. Eq. 175 (2001), 415-501.

GiVl-p2 J. Ginibre, G. Velo, Long range scattering and modified wave operators for the Wave-Schrodinger system, preprint.

GiVl-p4 J. Ginibre, G. Velo, Long range scattering and modified wave operators for the Wave-Schrodinger system III, preprint.

GiVl-p5 J. Ginibre, G. Velo, Scattering Theory for the Schr"odinger Equation in some external time dependent magnetic fields, preprint

GgMe1994 L. Glangetas, F. Merle, Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II., CMP 160 (1994), 349-389.

GgMe1994b L. Glangetas, F. Merle, Existence of self-similar blow-up solutions for Zakharov equation in dimension two I. CMP 160 (1994) 173-215.

GgMe1995 L. Glangetas, F. Merle, A geometric approach to existence of blow-up solutions, Prepublications Analyse Numerique, Universite Paris VI (1995)

Gs1973 R.T. Glassey, On the asymptotic behavior of non-linear wave equations, Trans. Amer. Math. Soc. 183 (1973) 187-200.

Gs1977 R.T. Glassey, On the blowing up of solutions to the Cauchy problem for nonlinear Schrodinger operators, J. Math. Phys. 8 (1977), 1794-1797.

Gs1977b R.T. Glassey, Asymptotic behavor of solutions to certain nonlinear Schrodinger-Hartree equations, CMP 53 (1977), 9-18.

Gs1981 R.T. Glassey, Existence in the large for \Box u = F(u) in two dimensions, Math Z. 178 (1981), 233-261.

Gs1981b R.T. Glassey, Finite time blow-up for solutions of non-linear wave equations, Math Z. 177 (1981), 323-340.

GsScf1988 R.T. Glassey, J. Schaeffer, Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data, CMP 119 (1988), 353-384.

GsScf1990 R.T. Glassey, J. Schaeffer, On the one and one-half dimensional relativistic Vlasov-Maxwell system, Math. Meth. Appl. Sci. 13 (1990), 169-179.

GsSr1979 R.T. Glassey, W. A. Strauss, Decay of a Yang-Mills field coupled to a scalar field, Comm. Math. Phys. 67 (1979), 51-67.

GsSr1979b R.T. Glassey, W. A. Strauss, Decay of classical Yang-Mills fields, Comm. Math. Phys. 65 (1979), 1-13.

GsSr1984 R.T. Glassey, W.A. Strauss, Remarks on collisionless plasmas, Contemp. Mathematics 28 (1984), 269-279.

GsSr1986 R.T. Glassey, W.A. Strauss, Large velocities in the relativistic Vlasov-Maxwell equations, J. Fac. Sci. Univ. Tokyo, Sect. IA, Math 36 (1986), 615-627.

GsSr1986b R.T. Glassey, W.A. Strauss Singularity formation in collisionless plasma could only occur at high velocities, Arch. Rat. Mech. Anal. 92 (1986), 56-90.

GsSr1987 R.T. Glassey, W.A. Strauss, High velocity particles in collisionless plasma, Math. Meth. in Appl. Sci. 9 (1987), 46-52.

GbScg-p M. Goldberg, W. Schlag, Dispersive estimates for Schrodinger operators in dimensions one and three, preprint.

Go1993 P. Godin, Lifespan of semilinear wave equations in two space dimensions, CPDE 18 (1993), 895-916.

Go1995 P. Godin, Global existence of solutions to some exterior radial quasilinear Cauchy-Dirichlet problems, Amer. J. Math. 117 (1995), 1475-1505.

Grf1990 J.M. Graf, Phase space analysis of the charge transfer model, Helv. Physica Acta 63 (1990), 107-138.

Grn1998 E. Grenier, Semiclassical limit of the nonlinear Schrodinger equation in small time, PAMS 126 (1998), 523-530.

Gl1988 M. Grillakis, Linearized instability for nonlinear Schrödinger and Klein-Gordon equations. Comm. Pure Appl. Math. 41 (1988), 747-774.

Gl1990 M. Grillakis, Regularity and asymptotic behaviour of the wave equation with a critical non-linearity, Ann. Math. 132 (1990), 485-509.

Gl1992 M. Grillakis, Regularity for the wave equation with a critical nonlinearity, Comm. Pure Appl. Math., 45 (1992), 749-774.

Gl1992b M. Grillakis, Some remarks on the regularity of wave equations with a critical nonlinearity. Nonlinear hyperbolic equations and field theory (Lake Como, 1990), 110-120, Pitman Res. Notes Math. Ser., 253, Longman Sci. Tech., Harlow, 1992.

Gl1994 M. Grillakis, A priori estimates and regularity of nonlinear waves, Proceed. Inter. Congress of Math. 1994, Birkhauser, 1187-1194.

Gl1998 M. Grillakis, Energy estimates and the wave map problem. Comm. Partial Differential Equations 23 (1998), 887-911.

Gl1999 M. Grillakis, The wave map problem. Current developments in mathematics, 1997 (Cambridge, MA), 227-230, Int. Press, Boston, MA, 1999.

Gl-p M. Grillakis, Classical solutions for the equivariant wave map in 1+2 dimensions, to appear in Indiana Univ. Math. J.

GlSaSr1982 M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry I, J. Funct. Anal. 74 (1987), 160-197.

GlSaSr1990 M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry II, J. Funct. Anal.94 (1990), 308-348.

GriSan-p P. Grinevich, P. Santini, The initial boundary value problem on the segment for the Nonlinear Schr\"odinger equation; the algebro-geometric approach. I, preprint.

Grs1966 L. Gross, The Cauchy problem for the coupled Maxwell and Dirac equations, CPAM 19 (1966), 1-15.

Gr-p2 A. Gruenrock, Some local wellposedness results for nonlinear Schroedinger equations below L^2, preprint.

Gr-p3 A. Gruenrock, A bilinear Airy- estimate with application to gKdV-3, preprint

Gr-p4 A. Gruenrock, An improved local well-posedness result for the modified KdV equation, preprint

Gu1980 C. Gu, On the Cauchy problem for harmonic maps defined on two-dimensional Minkowski space, Comm. Pure Appl. Math., 33 (1980), 727-737.

Gu1984 C. Gu, On the harmonic maps from R^{1,1} to S^{1,1}, Journal fur Mathematik 346 (1984), 101-109.

Gue2003 M. Guedda, Blowup of solutions to semilinear wave equations, EJDE 2003 (2003), 53, 1-5.

GusNaTsa-p S. Gustafson, K. Nakanishi, T. Tsai, Asymptotic Stability and Completeness in the Energy space for Nonlinear Schrodinger equations with small solitary waves, preprint.

GuoNkSr1996 Y. Guo, K. Nakamitsu, W. Strauss, Global finite energy solutions of the Maxwell-Schrodinger system, CMP 170 (1986), 181-196.

GuoTan1992 B. Guo, S. Tan, Cauchy problem for a generalized nonlinear dispersive equation, JPDE 5(4) (1992), 37-50

H

Har1990 J. Harmse, On Lebesgue space estimates for the wave equation, Indiana Univ. Math. J. 30 (1990), 229-248.

HasKod1987 A. Hasegawa, Y. Kodama, Nonlinear pulse propagation in a monomode dielectric guide, IEEE J. Quantum Elec. 23 (1987) 510-524.

Hm1972 H. Hasimoto, A soliton on a vortex filament, Journal of fluids mechanics 51 (1972), 477-485.

HslTaWun-p A. Hassell, T. Tao, J. Wunsch. A Strichartz inequality for the Schrodinger equation on non-trapping asymptotically conic manifolds, preprint.

Ha1990 N. Hayashi, Global existence of small analytic solutions to nonlinear Schrodinger equations, Duke Math J. 60 (1990), 717-727.

Ha1993 N. Hayashi, The initial value problem for the derivative nonlinear Schrodinger equation in the energy space, Nonlinear Anal. 20 (1993), 823-833.

Ha1995 N. Hayashi, Global existence of small solutions to quadratic nonlinear wave equations in an exterior domain, J. Funct. Anal. 131 (1995), 302-344.

Ha2000 N. Hayashi, Asymptotic behavior of time of solutions to nonlinear wave equation in an exterior domain. CPDE 25 (2000), 423-456.

Ha-p N. Hayashi, Local existence in time of small solutions to the Ishimori system, preprint.

HaKak1995 N. Hayashi, K. Kato, Regularity in time of solutions to nonlinear Schrodinger equations, J. Funct. Anal. 128 (1995), 253-277.

HaKakNm1998 N. Hayashi, K. Kato, P.I. Naumkin, On the scattering in Gevrey classes for the subcritical Hartree and Schrodinger equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 27 (1998), 483-497

HaMia1999 C. Miao, N. Hayashi, Global existence of small solutions to the genrealized derivative non-linear Schrodinger equation, Asymptotic Analysis 21 (1999), 133-147.

HaHr-p N. Hayashi, H. Hirata, Global existence of small solutions to nonlinear Schrodinger equations, preprint.

HaKaiNm1998 N. Hayashi, E.I. Kaikina, P.I. Naumkin, On the scattering theory for the cubic nonlinear Schrodinger and Hartree type equations in one space dimension, Hokkaido Math. J. 27 (1998), 651-667

HaKakOz1996 N. Hayashi; K, Kato; T. Ozawa, Dilation method and smoothing effects of solutions to the Benjamin-Ono equation. Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), no. 2, 273-285.

HaKakNm1998 N. Hayashi, K. Kato, P.I. Naumkin, On the scatterign in Gevrey classes for the subcritical Hartree and Schrodinger equations, Ann. Scoul. Norm. Sup. Pisa 27 (1998), 483-497.

HaNkTs1986 N. Hayashi, K. Nakamitsu, M. Tsutsumi, On solutions to the initial value problem for the nonlinear Schrodinger equations in one space dimension, Math Z. 192 (1986), 637-650.

HaNkTs1987 N. Hayashi, K. Nakamitsu, M. Tsutsumi, On solutions to the initial value problem for the nonlinear Schrodinger equations, J. Funct. Anal. 71 (1987), 218-245.

HaNm1997 N. Hayashi, P.I. Naumkin, Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation revisited. Discrete Contin. Dynam. Systems 3 (1997), no. 3, 383-400.

HaNm1998 N. Hayashi, P.I. Naumkin, Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations. Amer. J. Math. 120 (1998), 369-389.

HaNm1998b N. Hayashi, P.I. Naumkin, Remarks on scattering theory and large time asymptotics of solutions to Hartree type equations with a long range potential. SUT J. of Math. 34 (1998), 13-24.

HaNm1998c N. Hayashi, P.I. Naumkin, Large time asymptotics of solutions to the generalized Korteweg-de Vries equation. J. Funct. Anal. 159 (1998), no. 1, 110-136.

HaNm1998d N. Hayashi, P.I. Naumkin, Asymptotics and scattering problem for the generalized Korteweg-de Vries equation. Harmonic analysis and nonlinear partial differential equations (Japanese) (Kyoto, 1997). Surikaisekikenkyusho Kokyuroku No. 1059 (1998), 101-109.

HaNm1999 N. Hayashi, P.I. Naumkin, Large time asymptotics of solutions to the generalized Benjamin-Ono equation. Trans. Amer. Math. Soc. 351 (1999), no. 1, 109-130.

HaNm2001 N. Hayashi, P.I. Naumkin, Scattering theory and large time asymptotics of solutions to the Hartree type equations with a long range potential, Hokkaido Math. J. 30 (2001), 137-161.

HaNm2001b N. Hayashi, P.I. Naumkin, Asymptotic behaviour for Schrodinger equations with a quadratic nonlinearity in one space dimension, EJDE 2001 (2001), 54, 1-18.

HaNm2002 N. Hayashi, P.I. Naumkin, On the reduction of the modified Benjamin-Ono equation to the cubic derivative nonlinear Schrödinger equation. Discrete Contin. Dyn. Syst. 8 (2002), no. 1, 237-255.

HaNmOz1998 N. Hayashi, T. Ozawa, P.I. Naumkin, Scattering theory for the Hartree type equation, SIAM J. Math. Anal. 29 (1998), 1256-1267.

HaNmPi-p N. Hayashi, P.I. Naumkin, P.-N. Pipolo, Smoothing effect for some derivative nonlinear Schrodinger equations, preprint.

HaNmSau1999 N. Hayashi, P.I. Naumkin, J.C. Saut, Asymptotics for large time of global solutions to the generalized Kadomtsev-Petviashvili equation. Comm. Math. Phys. 201 (1999), no. 3, 577-590.

HaNmSau1999b N. Hayashi, P.I. Naumkin, J.C. Saut, Scattering problem and asymptotics for a relativistic nonlinear Schrödinger equation. Nonlinearity 12 (1999), no. 5, 1415-1425.

HaNmShiTon2004 N. Hayashi, P.I. Naumkin, A. Shimomura, S. Tonagawa, Modified wave operators for nonlinear Schrodinger equations in one and two dimensions, Electron. J. Diff. Eqns., Vol. 2004(2004), No. 62, pp. 1-16.

HaOz1988 N. Hayashi, T. Ozawa, Scattering theory in the weighted L^2(R^n) spaces for some Schrodinger equations, Ann. IHP, Physique theorique 48 (1988), 17-37.

HaOz1989 N. Hayashi, T. Ozawa, Smoothing effect for some Schrödinger equations. J. Funct. Anal. 85 (1989), no. 2, 307-348.

HaOz1992 N. Hayashi, T. Ozawa, On the derivative nonlinear Schrodinger equation, Phys D 55(1992), 14-36.

HaOz1994 N. Hayashi, T. Ozawa, Finite energy solutions of nonlinear Schrodinger equations of derivative type, SIAM J. Math. Anal. 25 (1994), 1488-1503.

HaOz1994b N. Hayashi, T. Ozawa, Remarks on nonlinear Schrodinger equations in one space dimension, Diff. Integ. Eq. 7 (1994), 453-461.

HaOz1994c N. Hayashi, T. Ozawa, Modified wave operators for the derivative nonlinear Schrodinger equation, Math. Ann. 298 (1994), 557-576.

HaOz1995 N. Hayashi, T. Ozawa, Schrodinger equations with nonlinearity of integral time, Discrete and Continuous Dynamical Systems 1 (1995), 475-484.

HaSau1995 N. Hayashi, J.C. Saut, Global existence of small solutions to the Davey-Stewartson and the Ishimori systems, DIE 8 (1995), 1657-1675.

HaTs1986 N. Hayashi, Y. Tsutsumi, L^infty(R^n) decay of classical solutions for nonlinear Schrodinger equations, Proc. Royal Soc. Edin. 104 (1986), 309-327.

HaTs1987 N. Hayashi, Y. Tsutsumi, Scattering theory for Hartree type equations, Ann. Inst. Henri Poincare, Phys. Th. 47 (1987), 187-213.

HaTs1987b N. Hayashi, Y. Tsutsumi, Remarks on the scattering problem for nonlinear Schrodinger equations, LNM 1285, 162-168, Springer, Berlin-New York, 1987.

HaWl1987 N. Hayashi, W. von Wahl, On the global strong solutions of coupled Klein-Gordon-Schrodinger equations, J. Math. Soc. Japan 39 (1987), 489-497.

He1991 F. Helein, Regularity of weakly harmonic maps from a surface into a manifold with symmetries, Manusc. Math. 70 (1991), 203-218.

Hi1998 K. Hidano, Nonlinear small data scattering for the wave equation in R^{4+1}, J. Math. Soc. Japan 50 (1998), 253-292

Hi-p1 K. Hidano, Small data scattering and blow-up for the wave equation with a cubic convolution, Funkcial. Ekvac., to appear.

Hi-p2 K. Hidano, Scattering and self-similar solutions for the wave equation, to appear.

Hi-p3 K. Hidano, Scattering for the non-linear wave equation in the finite energy and conformal charge space, preprint.

Hi-p4 K. Hidano, An elementary proof of global or almost global existence for quasi-linear wave equations, preprint.

HiYk-p K. Hidano, K. Yokoyama, A remark on the almost global existence theorems of Keel, Smith, and Sogge, preprint.

HiYk-p2 K. Hidano, K. Yokoyama, A new proof of the global existence theorem of Klainerman, preprint.

HimMis2001 A. Himonas, G. Misiolek, A priori estimates for Schrodinger type multipliers, Illinois J. Math. 45 (2001), 631-640.

Hog1985 S.J. Hogan, The fourth order evolution equation for deep-water gravity-capillary waves, Proc. Roy. Soc. London Ser. A. 402 (1985), 359-372.

Hp1994 J. Hoppe, Some classical solutions of relativistic membrane equations in 4-space-time dimensions, Phys. Lett. B 329 1 (1994), 10-14.

Ho1988 L. Hormander, L^1, L^\infty estimates for the wave operator, Analyse math. et appl., Gauthier-Villars, Paris, 1988, 211-234

Ho1997 L. Hormander, Lectures on nonlinear hyperbolic differential equations, Mathematiques & Applications, 26. Springer-Verlag, 1997.

Hg1995 A. Hoshiga, The initial value problems for quasilinear wave equations in two space dimensions with small data, Adv. Math. Sci. Appl. 5 (1995), 67-89.

Hg1998 A. Hoshiga, The lifespan of solutions to quasilinear hyperbolic systems in the critical case, Funkcial. Ekvac. 41 (1998), 167-188.

HgKu2000 A. Hoshiga, H. Kubo, Global small amplitude solutions of nonlinear hyperbolic systems with a critical exponent under the null condition, SIAM J. Math. Anal 31 (2000), 486-513.

Hs1997 T. Hoshiro, On weighted L^2 estimates of solutions to wave equations, J. Anal. Math. 72 (1997), 127\u2014140.

Hs1999 T. Hoshiro, Mourre's method and smoothing properties of dispersive equations, Comm. Math. Phys. 202 (1999), 255-265.

Hs-p T. Hoshiro, Decay and regularity for dispersive equations with constant coefficients, preprint.

HuKaMar1977 T. Hughes, T. Kato, J. Marsden, Well-posed quasilinear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity, Arch. Ration. Mech. Anal. (1977) 63(3), 273-294.

HuoGuo-p Z. Huo, B. Guo, The well-posedness of the Cauchy problem for the generalized nonlinear dispersive equation, preprint.

I

Ic1984 W. Ichinose, Some remarks on the Cauchy problem for Schrodinger type equations, Osaka J. Math 21 (1984), 565-581.

Ik1968 M. Ikawa, Mixed problems for hyperbolic equations of second order, J. Math. Soc. Japan 20 (1968), 580-608.

Ik1982 M. Ikawa, Decay of solutions of the wave equations to the exterior of two convex bodies, Osaka J. Math. 19 (1982), 459-509.

Ik1998 M. Ikawa, Decay of solutions to the wave equation to the exterior of several convex bodies, Ann. Inst. Fourier (Grenoble), 38 (1998), 113-146.

IonKn-p A. Ionescu. C. Kenig, L^p Carleman inequalities and uniqueness of solutions of nonlinear Schrodinger equations

Io1986 R.J. Iorio Jr., On the Cauchy problem for the Benjamin-Ono equation, CPDE 11 (1986), 1031-1181.

IoNu1998 R. J. Iorio Jr., W.V.L. Nunes, On equations of KP-type, Proc. Roy. Soc. Edinburgh A. 128 (1998), 725-743.

Isk1993 V. Isakov, Carleman type estimates in an anisotropic case and applications, JDE 105 (1993), 217\u2014238.

IsLopMj-p P. Isaza, J. Lopez, J. Mejia, The Cauchy problem for the Kadomtsev-Petviashvili (KPII) equation in three space dimensions, preprint

IsMj2001 P. Isaza, J. Mejia, Local and global Cauchy problems for the KP-II equations in Sobolev spaces of negative index, CPDE 26 (2001), 1027-1054

IsMj2003 P. Isaza, J. Mejia, Global solution for the Kadomtsev-Petviashvili equation (KPII) in anisotropic Sobolev spaces of negative index, EJDE 2003 (2003) 68, 1-12.

IsMjStb1994 P. Isaza, J. Mejia, V. Stallbohm, A regularity theorem for the Kadomtsev-Petviashvili equation with periodic boundary conditions, Nonlinear Anal. 23 (1994), 683-687.

IsMjStb1995 P. Isaza, J. Mejia, V. Stallbohm, Local solution for the Kadomtsev-Petviashvili equation in R^2,J. Math. Anal. Appl. 196 (1995), no. 2, 566-587.

IsMjStb1997 P. Isaza, J. Mejia, V. Stallbohm, Regularizing effects for the linearized Kadomtsev-Petviashvili (KP) equation.Rev. Colombiana Mat. 31 (1997), no. 1, 37-61.

IsMjStb2001 P. Isaza, J. Mejia, V. Stallbohm, El problema de Cauchy para la ecuacion de Kadomtsev-Petviashvili (KP-II) en espacios de Sobolev H^s, s > 0, DIE 14 (2001) 529-557.

IbLie-p J. Isenberg, S. Liebling, Singularity formulation in 2+1 Wave maps, preprint.

Im1984 Y. Ishimori, Multivortex solutions of a two-dimensional nonlinear wave equation, Progr. Theoret. Phys. 72 (1984), 33-37.

J

Je1980 A. Jensen, Spectral properties of Schrodinger operators and time decay of the wave functions Results in L^2(R^m), m > 5, Duke Math J. 47 (1980), 57-80.

Je1984 A. Jensen, Spectral properties of Schrodinger operators and time decay of the wave functions Results in L^2(R^4), JMAA 101 (1984), 397-422.

JeKa1980 A. Jensen, T. Kato, Spectral properties of Schrodinger operators and time decay of the wave functions, Duke Math J. 46 (1979), 583-611.

JeNc2001 A. Jensen, G. Nenciu, A unified approach to resolvent expansions at thresholds, Rev. Math. Phys. 13 (2001), 717-754.

JeYa2002 A. Jensen, K. Yajima, A remark on L^p boundedness of wave operators for two-dimensional Schrodinger operators, CMP 225 (2002), 633-637.

Je1986 A. Jensen, Commutator methods and a smoothing property of the Schrodinger evolution group, Math. Z. 191 (1986), 53-59.

JiZz2003 H. Jiao, Z. Zhou, An elementary proof of the blowup for a semilinear wave equation in high space dimensions, JDE 189 (2003), 355-365.

Jo1979 F. John, Blow-up of solutions of non-linear wave equations in three dimensions, Manuscript. Math. 28 (1979), 235-268.

Jo1981 F. John, Blow-up for quasilinear wave equations in three space dimensions, CPAM 34 (1981), 29-51.

Jo1985 F. John, Blowup of radial solutions of u_tt = c^2(u_t) Delta u in three space dimensions, Mat. Appl. Comput. 4 (1985), 3-18.

Jo1987 F. John, Existence for large times of strict solutions to nonlinear wave equations in three space dimension for small data, CPAM 40 (1987), 79-109.

Jo1990 F. John, Nonlinear wave equations, formulation of singularities, University Lecture Series, AMS 1990.

JoKl1984 F. John, S. Klainerman, Almost global existence to nonlinear wave equations in three space dimensions, CPAM 37 (1984), 443-455.

Jor1961 K. Jorgens, Das Anfangswertproblem im Grossen fur eine Klasse nichtlinearer Wellengleichungen, Math. Z. 77 (1961), 295-308.

JouSfSo1991 J.L. Journe, A. Soffer, C. Sogge, Decay estimates for Schrodinger operators, CPAM 44 (1991), 573-604.

K

KdPv1970 B.B. Kadomtsev, V.I. Petviashvili, On the stability of solitary waves in weakly dispersive media, Soviet Phys. Dokl. 15 (1970), 539-541.

Kt1990 L. Kapitanski, Some Generalizations of the Strichartz-Brenner Inequality, Leningrad Math. J., 1 (1990), 693-676.

Kt1992 L. Kapitanski, The Cauchy problem for semilinear wave equations II and III., J. Soviet Math. 62 (1992), 2746-2777.

Kt1994 L. Kapitanski, Weak and Yet Weaker Solutions of Semilinear Wave Equations, Comm. Part. Diff. Eq., 19 (1994), 1629-1676.

Kt1994b L. Kapitanski, Global and unique weak solutions of nonlinear wave equations, Math. Res. Letters, 1 (1994), 211-223.

Kp1993 T. Kappeler, Solutions to the Korteweg-de Vries equation with irregular initial profile, Comm. Partial Differential Equations 11 (1986), no. 9, 927-945.

KpMrTp-p T. Kappeler, C, Mohr, P. Topalov, Birkhoff coordinates for KdV on phase spaces of distributions, preprint

KpTp-p T. Kappeler, P. Topalov, Global well-posedness of KdV in H^{-1}(T,R), preprint

KpTp-p2 T. Kappeler, P. Topalov, Global well-posedness of mKdV in L^2(T,R), preprint

Ky1993 S. Katayama, Global existence for systems of nonlinear wave equations in two space dimensions, Publ. RIMS Kyoto U. 29 (1993), 1021-1041.

KyTs1994 S. Katayama, Y. Tsutsumi, Global existence of solutions for nonlinear Schrödinger equations in one space dimension. Comm. Partial Differential Equations 19 (1994), 1971-1997.

KakOg-p K. Kato, T. Ogawa, Analyticity and smoothing effect for the Korteweg de Vries equation with single point singularity, preprint.

Ka1975 T. Kato, Quasilinear equations of evolution, with applications to partial differential equations, Springer Lecture Notes in Math. 448 (1975), 27-50

Ka1979 T. Kato, On the Korteweg-de Vries equation, Manuscripta Math. 29 (1979), 89-99

Ka1979b T. Kato, The Cauchy problem for the Korteweg-de Vries equation, Pitman Research Notes in Math. 53 (1979), 293-307

Ka1980 T. Kato, Blow-up of solutions of some nonlinear hyperbolic equations, Comm. Pure Appl. Math. 33 (1980), 501-505.

Ka1983 T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Adv. in Math. Suppl. Stud., Stud. in Appl. Math. 8 (1983), 93-128.

Ka1986 T. Kato, On nonlinear Schrodinger equations, Ann. Inst. H. Poincare Phys. Theor. 46 (1986), 113-129.

Ka1989 T. Kato, Nonlinear Schrödinger equation, Schrödinger operators, Lecture Notes in Physics, 345 (H. Holden and A. Jensen, eds.), Springer-Verlag, 1989, pp. 218-263.

Ka1994 T. Kato, An L^{q,r} theory for nonlinear Schrodinger equations, Spectral and scattering theory and applications, Adv. Stud. Pure Math. 23 (1994), 223-238.

Ka1995 T. Kato, On nonlinear Schrodinger equations II. H^s solutions and unconditional well-posedness, J. Anal. Math. 67 (1995), 281-306.

KaPo1988 T. Kato, G. Ponce, Commutator estimates and the Euler and Navier-Stokes equations, CPAM 41 (1988), 891-907

KaYa1989 T. Kato, K. Yajima, Some examples of smooth operators and the associated smoothing effect, Rev. Math. Phys. 1 (1989), 481-496.

KauNe1978 D. J. Kaup, A. C. Newell, An exact solution for a derivative nonlinear Schrodinger equation, J. Math. Phys. 19 (1978), 798-801.

Kav1987 O. Kavian, A remark on the blowing up of solutions to the Cauchy problem for nonlinear Schrodinger equations, TAMS 299 (1987), 193-203.

Ke1997 M. Keel, Global existence for critical power Yang-Mills-Higgs equations in R^{3+1}, Commun. in PDE 22 (1997), 1167\u20131227

KeSmhSo2000 M. Keel, H. Smith, C. Sogge, On global existence for nonlinear wave equations outside convex obstacles, Am. J. Math 122 (2000), 805\u2013842.

KeSmhSo-p M. Keel, H. Smith, C. Sogge, On global existence for a quasilinear wave equation outside of star-shaped domains, preprint.

KeSmhSo-p2 M. Keel, H. Smith, C. Sogge, Almost global existence for some semilinear wave equations, J. D\u2019Analyse, 87 (2002), 265-279.

KeSmhSo-p3 M. Keel, H. Smith, C. Sogge, Almost global existence for quasilinear wave equations in three space dimensions, preprint.

KeTa-p M. Keel, T. Tao, Global well-posedness for large data for the Maxwell-Klein-Gordon equation below the energy norm, in preparation.

Kel1957 J. Keller, On solutions of nonlinear wave equations, CPAM 10 (1957), 523-530.

Kn-p C. Kenig, On the local and global theory of the KP-I equation, preprint.

KnKoe-p C. Kenig, K. Koenig, On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations, preprint.

KnPoVe1989 C. Kenig, G. Ponce, L. Vega, On the (generalized) Korteweg-de Vries equation, Duke Math. J. 59 (1989), 585-610.

KnPoVe1990 C. Kenig, G. Ponce, L. Vega, The initial value problem for a class of nonlinear dispersive equations. Functional-analytic methods for partial differential equations (Tokyo, 1989), 141-156, Lecture Notes in Math., 1450, Springer, Berlin, 1990.

KnPoVe1991 C. Kenig, G. Ponce, L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991), 33-69

KnPoVe1991b C. Kenig, G. Ponce, L. Vega, Well-posedness of the initial value problem for the KdV equation, J. Amer. Math. Soc. 4 (1991), 323-347

KnPoVe1993 C. Kenig, G. Ponce, L. Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math. 46 (1993), 527-560.

KnPoVe1993b C. Kenig, G. Ponce, L. Vega, The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices, Duke Math. J. 71 (1993), 1-21.

KnPoVe1993c C. Kenig, G. Ponce, L. Vega, Small solutions to nonlinear Schrodinger equations, Ann. Inst. H. Poincare Anal. Nonlineaire 10 (1993), 255-288.

KnPoVe1994 C. Kenig, G. Ponce, L. Vega, Higher-order non-linear dispersive equations, Proc. Amer. Math. Soc. 122 (1994), 157-166.

KnPoVe1994b C. Kenig, G. Ponce, L. Vega, On the genrealized Benjamin-Ono equation,TAMS 342 (1994), 155-172.

KnPoVe1995 C. Kenig, G. Ponce, L. Vega, On the IVP for the nonlinear Schrodinger equations, Harmonic Analysis and operator theory (Caracas 1994), Contemporary Math. AMS Providence RI 189 (1995), 353-367.

KnPoVe1995b C. Kenig, G. Ponce, L. Vega, On the Zakharov and Zakharov-Suhulman systems, J. Funct. Anal. 127 (1995), 204-234.

KnPoVe1996b C. Kenig, G. Ponce, L. Vega, Quadratic forms for the 1-D semilinear Schrodinger equation, Trans. Amer. Math. Soc. 346 (1996), 3323-3353.

KnPoVe1997 C. Kenig, G. Ponce, L. Vega, Global solutions for the KdV equation with unbounded data. J. Differential Equations 139 (1997), 339-364.

KnPoVe1997b C. Kenig, G. Ponce, L. Vega, On the smoothing properties of some dispersive hyperbolic systems. Nonlinear waves (Sapporo, 1995), 221-229, GAKUTO Internat. Ser. Math. Sci. Appl., 10, Gakkotosho, Tokyo, 1997.

KnPoVe1997c C. Kenig, G. Ponce, L. Vega, On the Cauchy problem for linear Schrödinger systems with variable coefficient lower order terms. Harmonic analysis and number theory (Montreal, PQ, 1996), 205-227, CMS Conf. Proc., 21, Amer. Math. Soc., Providence, RI, 1997.

KnPoVe1998 C. Kenig, G. Ponce, L. Vega, Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations. Invent. Math. 134 (1998), 489-545.

KnPoVe2000 C. Kenig, G. Ponce, L. Vega, On the initial value problem for the Ishimori system, Ann. Henri Poincaré 1 (2000), 341-384.

• kdv_counter.dvi KnPoVe2001 C. Kenig, G. Ponce, L. Vega, [kdv_counter.dvi On the ill-posedness of some canonical dispersive equations], Duke Math. J. 106 (2001), 617-633.

KnPoVe2003 C. Kenig, G. Ponce, L. Vega, On unique continuation for the nonlinear Schrodinger equations, CPAM 56 (2003), 1247-1262

KnPoVe-p C. Kenig, G. Ponce, L. Vega, The Cauchy problem for quasilinear Schrodinger equations, preprint.

KnPoVe-p2 C. Kenig, G. Ponce, L. Vega, Global well-posedness for semi-linear wave equations, preprint.

KnPoVe-p4 C. Kenig, G. Ponce, L. Vega, On the unique continuation of solutions to the gKdV equation, preprint.

KnPoVe-p5 C. Kenig, G. Ponce, L. Vega, On the uniqueness of solutions of higher order nonlinear dispersive equations, preprint.

KnPoRolVe-p C. Kenig, G. Ponce, C. Rolvung, L. Vega, Local existence theory for the generalized nonlinear Schrodinger equations, preprint.

KnRu1983 C. Kenig, A. Ruiz, A strong type (2,2) estimate for the maximal function associated to the Schrodinger equation, TAMS 280 (1983), 239-246.

KnRuSo1987 C. Kenig, A. Ruiz, C. Sogge, Uniform Sobolev inequalities and unique continuation theorems for second order constant coefficient differential operators, Duke Math. J. 55 (1987), 329-347.

KnSo1988 C. Kenig, C. Sogge, A note on unique continuation for Schrodinger\u2019s operator, Proc. AMS 103 (1988), 543\u2014546.

KnSt1997 C. Kenig, G. Staffilani, Local well-posedness for higher-order nonlinear dispersive systems, JFAA 3 (1997), 417-433.

KeWg1998 C. Kenig, W. Wang, Existence of local smooth solution for a generalized Zakharov system, JFAA 4 (1998), 469-490.

Ker2002 S. Keraani, Semiclassical limit for a class of Nonlinear Schrodinger Equations with potential, CPDE 27 (2002), 693-704.

KiLit2003 S. Kichenassamy, W. Littman, Blow-up surfaces for nonlinear wave equations I, CPDE 18 (1993), 431-452.

KiLit2003b S. Kichenassamy, W. Littman, Blow-up surfaces for nonlinear wave equations II, CPDE 18 (1993), 1869-1899.

Kl1983 S. Klainerman, Long Time behavior of solutions to nonlinear wave equations, Proc. ICM Warsawa 1983.

Kl1985 S. Klainerman, Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, Comm. Pure Appl. Math. 38 (1985), 631-641.

Kl1985b S. Klainerman, Uniform decay estimate and the Lorentz invariance of the classical wave equations, CPAM 38 (1985), 321-332.

Kl1986 S. Klainerman, The null condition and global existence to nonlinear wave equations, Nonlinear systems of PDE in applied math. I (Santa Fe 1984), LNM, AMS Providence RI 23 (1986), 293-326.

Kl1987 S. Klainerman, Remarks on the global Sobolev inequalities in the Minkowski space R^{n+1}, CPAM 40 (1987), 111-117.

Kl1997 S. Klainerman, On the regularity of classical field theories in Minkowski space-time R^{3+1}, Prog. in Nonlin. Diff. Eq. and their Applic., 29, (1997), Birkh\"auser, 113-150.

Kl-p S. Klainerman, PDE as a unified subject, preprint.

KlMa1993 S. Klainerman, M. Machedon, Space-time Estimates for Null Forms and the Local Existence Theorem, Comm. Pure Appl. Math., 46 (1993), 1221-1268.

KlMa1994 S. Klainerman, M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy, Duke Math. J. 74 (1994), 19-44.

KlMa1995 S. Klainerman, M. Machedon, Finite energy solutions of the Yang-Mills equations in R^{3+1}. Ann. of Math. 142 (1995) , 93-116.

KlMa1995b S. Klainerman, M. Machedon, Smoothing estimates for null forms and applications, Duke Math J. 81 (1995), 99-103.

KlMa1996 S. Klainerman, M. Machedon, Remark on Strichartz-type inequalities. With appendices by Jean Bourgain and Daniel Tataru. Int. Math. Research Notices5 (1996), 201-220.

KlMa1996b S. Klainerman, M. Machedon, Estimates for null forms and the spaces H_{s,\delta}, Int. Math. Research Notices 17 (1996), 853-866.

KlMa1997 S. Klainerman, M. Machedon, On the optimal local regularity for gauge field theories, Diff. and Integral Eq. 10 (1997), 1019-1030.

KlMa1997b S. Klainerman, M. Machedon, On the regularity properties of a model problem related to wave maps, Duke Math. J. 87 (1997), 553-589.

KlMa1998 S. Klainerman, M. Machedon, On the algebraic properties of the $H^{n/2,1/2}$ spaces. Internat. Math. Res. Notices 15 (1998)765-774.

KlNi1999 S. Klainerman, F. Nicolò, On local and global aspects of the Cauchy problem in general relativity. Classical Quantum Gravity 16 (1999), no. 8, R73-R157

KlNi2003 S. Klainerman, F. Nicolo, The evolution problem in general relativity, Birkhauser 2003

KlNi-p S. Klainerman, F. Nicolo, Peeling properties of asymptotically flat solutions to the Einstein vacuum equations, preprint.

KlPo1983 S. Klainerman, G. Ponce, Global small amplitude solutions to nonlinear evolution equations, CPAM 36 (1983), 133-141.

KlRo-p S. Klainerman, I. Rodnianski, On the global regularity of wave maps in the critical Sobolev norm, preprint.

KlRo-p2 S. Klainerman, I. Rodnianski, Improved Local Well Posedness for Quasilinear Wave Equations in Dimension Three, preprint.

KlRo-p3 S. Klainerman, I. Rodnianski, Rough solution for the Einstein Vacuum equations, preprint

KlRo-p4 S. Klainerman, I. Rodnianski, The causal structure of microlocalized Einstein metrics, preprint

KlRo-p5 S. Klainerman, I. Rodnianski, Ricci defects of microlocalized Einstein metrics, preprint

KlRo-p6 S. Klainerman, I. Rodnianski, Causal Geometry of Einstein-Vacuum Spacetimes with Finite Curvature Flux, preprint

KlRo-p7 S. Klainerman, I. Rodnianski, Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux, preprint

KlRo-p8 S. Klainerman, I. Rodnianski, A geometric approach to the Littlewood-Paley theory, preprint.

KlRoTa-p2 S. Klainerman, I. Rodnianski, T. Tao, A physical space approach to wave equation bilinear estimates, preprint.

KlSb1997 S. Klainerman, S. Selberg, Remark on the optimal regularity for equations of wave maps type, C.P.D.E., 22 (1997), 901-918.

KlSb-p S. Klainerman, S. Selberg, Bilinear estimates and applications to nonlinear wave equations, preprint.

KlSi1996 S. Klainerman, T. Sideris, On almost global existence for nonrelativistic wave equations in 3D, CPAM 49 (1996), 307-321.

KlSt2002 S. Klainerman, G. Staffilani, A new approach to study the Vlasov-Maxwell system, CPAA 1 (2002), 103-125.

KlTt1999 S. Klainerman, D. Tataru, On the optimal regularity for Yang-Mills equations in R^{4+1}, J. Amer. Math. Soc. 12 (1999), 93-116.

Kg-p J. Krieger, Global regularity of wave maps from R^{3+1} to a Riemann surface, preprint.

KocTz-p H. Koch, N. Tzvetkov, On the local well-posedness of the Benjamin-Ono equation in H^s(R), IMRN 2003:26.

KocTz-p2 H. Koch, N. Tzvetkov, Nonlinear wave interactions the Benjamin-Ono equation, preprint.

Kod1985 Y. Kodama, Optical solitons in a monomode fiber, J. Statistical Phys. 39 (1985), 597-614.

KolNewStrQi2000 E. B. Kolomeisky, T. J. Newman, J.P. Straley, X. Qi, Low dimensional Bose Liquids: Beyond the Gross-Pitaevski approximation, Phys. Review Letters 85 (2000), 1146-1149.

KonMat1989 B. Konopelchenko, B. Matkarimov, On the inverse scattering transform of the Ishimori equations, Phys. Lett. A 135 (1989), 183-189.

KozOgTns2001 H. Kozono, T. Ogawa, H. Tanisaka, Well-posedness for the Benjamin equations, J. Korean Math. Soc. 38 (2001) 6, 1205-1234.

KwVr1895 D.J. Korteweg, G. de Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag. 539 (1895), 422-443.

Ks1992 R. Kosecki, The unit condition and global existence for a class of nonlinear Klein-Gordon equations, JDE 100 (1992), 257-268.

Ko1987 M. Kovalyov, Long-time behavior of solutions of a system of nonlinear wave equations, Comm. Part. Diff. Eq., 12 (1987),471-501. With Errata in CPDE 18 (1993) 1971-1976.

Ko1989 M. Kovalyov, Resonance type behaviour in a system of nonlinear wave equations, JDE 77 (1989), 73-83.

Kri2003 J. Krieger, Global regularity of wave maps from R^{3+1} to H^2, CMP 238 (2003), 333-366.

Kri-p J. Krieger, Global regularity of wave maps from R^{2+1} to H^2. Small energy, preprint.

Kru1978 M. Kruskal, The birth of the soliton, Research Notes in Mathematics, 26 (1978), 1-8.

KrFa1983 S. Kruzhkov, A. Faminskii, Generalized solutions of the Korteweg-de Vries equation (Russian), Mat. Sb. (N.S.) 120 (1983), 296-425; English translation in Math USSR Sbornik 48 (1984), 391-421.

KuKb1995 H. Kubo, K. Kubota, Asymptotic behaviors of radially symmetric solutions of Box u = |u|^p for super critical values p in odd space dimensions, Hokkaido M ath J. 24 (1995), 287-336

Kuk1995 S B Kuksin, Infinite-dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDE's, Comm. Math. Physics 167 (1995) pp. 531-552.

Kuk1995b S B Kuksin, On squeezing and flow of energy for nonlinear wave equations GAFA 5 (1995) pp. 668-701

Kz-p M. Kunze, A variational problem with lack of compactness related to the Strichartz inequality, preprint.

Kz-p2 M. Kunze, On the existence of a maximizer for the Strichartz inequality, preprint.

L

LabSf1999 I. Laba, A. Soffer, Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds, Helv. Phys. Acta 72 (1999), no. 4, 274--294.

Lad1999 R. Ladhari, Petites solutions d'equations dondes quasilineaires en dimension deux d'espace, These, Universite Paris-Sud, 1999.

LaSh1981 O.A. Ladyzhenskaya, V.I. Shubov, Unique solvability of the Cauchy problem for the equations of the two dimensional chiral fields, taking values in complete Riemann manifolds, J. Soviet Math., 25 (1984), 855-864. (English Trans. of 1981 Article.)

LanPapSucSup1988 M. Landman, G. Papanicolaou, C. Sulem, P-L. Sulem, Rate of blowup for solutions of the nonlinear Schrodinger equation at critical dimension, Phys. Rev. A 38 (1988), 3837-3843

Lau1992 C. Laurey, The Cauchy problem for a third order nonlinear Schrodinger equation, CRAS Paris Serie I 315 (1992), 165-168.

Lau1997 C. Laurey, The Cauchy problem for a third order nonlinear Schrodinger equation, Nonlinear Analysis, TMA 29 (1997), 121-158.

Lau2001 C. Laurey, On a nonlinear dispersive equation with time-dependent coefficients, Adv. Diff. Eq. 6 (2001), 577-612.

Lau-p C. Laurey, The Cauchy problem for a generalized Zakharov system, preprint.

Lx1968 P. Lax, Integrals of nonlinear equations of evolution and solitary waves, CPAM 21 (1968), 467-490.

LxPh1989 P. Lax, R. Phillips, Scattering theory, revised edition, Acad. Press., San Diego (1989)

LxMzPh1963 P. Lax, C. Morawetz, R. Phillips, Exponential decay of solutions to the wave equation in the exterior of a star-shaped obstacle, CPAM 16 (1963), 477-486.

Leb1992 G. Lebeau, Controle de l'equation de Schrodinger, J. Math. Pures et Appliquees 71 (1992), 267-291.

Leb1992b G. Lebeau, Singularites de solutions d'equations d'ondes semi-lineaires, Annals Scientifiques de l'ENS 25 (1992), 201-231.

Leb2000 G. Lebeau, Optique nonlineaire et ondes sur critiques (Nonlinear Optics and supercritical waves), Seminaire: Equations aux Derivees Partielles, 1991-2000, Exp. No. IV.

Leb2002 G. Lebeau, Nonlinear optics and supercritical wave equation, Bull. Soc. Roy. Sci. Liege, 70 (2002), 267-306.Hommage a Pascal Laubin.

Le1989 J. H. Lee, Global solvability of the derivative nonlinear Schrodinger equation, TAMS 314 (1989), 107-118

Lev1990 H. Levine, The role of critical exponents in blowup theorems, SIAM Rev. 32 (1990), 262-288.

LhLin2003 H. Li, C. Lin, Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems, Electron. J. Diff. Eqns., Vol. 2003(2003), No. 93, pp. 1-17.

LtYu1991 T. Li, X. Yu, Lifespan of classical solutions to fully nonlinear wave equations, CPDE 16 (1991), 909-940.

LtZh1993 T. Li, Y. Zhou, Life-span of classical solutions to fully nonlinear wave equations in two space dmensions II, J. PDE 6 (1) (1993), 17-38.

LtZh1994 T. Li, Y. Zhou, Life-span of classical solutions to nonlinear wave equations in two space dimensions, J. Math. Pure et Appl. 73(3) (1994), 223-249.

LtZh1995 T. Li, Y. Zhou, A note on the life-span of classical solutions to nonlinear wave equations in four space dimensions, Indiana U. Math. J. 44 (1995), 1207-1248.

LimPo-p W. Lim, G. Ponce, On the initial value problem for one-dimensional quasilinear Schrodinger equations, preprint.

LnSr1978 J. Lin, W. Strauss, Decay and scattering of solutions of nonlinear Schrodinger equation, JFA 30 (1978), 245-263.

LiPo1993 F. Linares, G. Ponce, On the Davey-Stewartson systems, Annales de l'I.H.P. Analhyse nonlineaire 10 (1993), 523-548.

Li1999 F. Linares, L^2Global well-posedness of the initial value problem associated with the Benjamin equation, JDE 152 (1999), 1425-1433.

Lb1990 H. Lindblad, On the lifespan of solutions to nonlinear wave equations with small initial data, CPAM 43 (1990), 445-472.

Lb1992 H. Lindblad, Global solutions of nonlinear wave equations, CPAM 45 (9) (1992), 1063-1096.

Lb1993 H. Lindblad, A Sharp Counterexample to Local Existence of Low Regularity Solutions to Nonlinear Wave Equations, Duke Math J., 72, (1993), 503-539.

Lb1996 H. Lindblad, Counterexamples to local existence for semi-linear wave equations, Amer. J. Math. 118 (1996), 1-16.

Lp-p3 H. Lindblad, Well-posedness for the motion of an incompressible liquid with free surface boundary, preprint.

LbRo2003 H. Lindblad, I. Rodnianski, The weak null condition for Einstein\u2019s equations, C.R. Math. Acad. Sci. Paris 336 (2003), 901-906.

LbRo-p H. Lindblad, I. Rodnianski, Global existence in the Einstein Vacuum equations in wave co-ordinates, preprint.

LbSf-p H. Lindblad, A. Soffer, A remark on long-range scattering for the nonlinear Klein-Gordon equation, preprint.

LbSo1995 H. Lindblad, C. Sogge, On Existence and Scattering with Minimal Regularity for Semilinear Wave Equations, J. Func. Anal., 130 (1995), 357-426.

LbSo1996 H. Lindblad, C. Sogge, Restriction theorems and semilinear Klein-Gordon equations in (1+3) dimensions, Duke Math. J. 85 (1996), 227-252.

Liu1989 Y. Liu, The Cauchy problem for a class of nonlinear Schrodinger equations, J. Appl. Math. 4 (1989), 102-107.

Liu1991 Y. Liu, On the asymptotic behavior of solutions for a nonlinear Schrodinger equation, Chinese Annals Math. 12A (1991), 19-25.

Liu1993 Y. Liu, Instability of solitary waves for generalized Boussinesq equations, J. Dynamics and Diff. Eq. 5 (1993), 537-558.

Liu1995 Y. Liu, Instability and blowup of solutions to a generalized Boussinesq equation, Siam J. Math Anal 26 (1995), 1527-1546.

Liu1997 Y. Liu, Dispersion of small solutions of a generalized Boussinesq equation, JFA 147 (1997), 51-68.

Liu2000 Y. Liu, Strong instability of solitary wave solutions of a generalized Boussinesq equation, JDE 164 (2000), 223-239.

Liu2001 Y. Liu, Blowup and strong instability of solitary-wave solutions to a generalized Kadomtsev-Petviashvili equation, TAMS 353 (2001), 191-208.

Liu2002 Y. Liu, Blow-up and strong instability of solitary wave solutions of Kadomtsev-Petviashvili equations in three dimensions, JDE 180 (2002), 153-170.

LiuWgx1997 Y. Liu, X.P. Wang, Nonlinear stability of solitary waves of a generalized Kadomtsev-Petviashvili equation, CMP 183 (1997), 253-266.

M

MaStz-p M. Machedon, J. Sterbenz, Optimal well-posedness for the Maxwell-Klein-Gordon equations in 3+1 dimensions, preprint.

Mac-p S. Machihara, The nonrelativistic limit of the nonlinear Klein-Gordon equation, to appear, Funkcial. Ekvac.

MacNkrNaOz-p S. Machihara, M. Nakamura, K. Nakanishi, T. Ozawa, Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation, preprint.

MacNaOz-p2 S. Machihara, K. Nakanishi, T. Ozawa, Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation, preprint.

MacNaOz-p S. Machihara, K. Nakanishi, T. Ozawa, Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations, preprint.

MadSac1993 J. Maddocks, R. Sachs, On the stability of KdV multi-solitons, CPAM 46 (1993) 867-901

Ms1981 B. Marshall, Mixed-norm estimates for the Klein-Gordon equation, in Proc. Conf. Harmonic Anal. Antoni Zygmund, Wardsworth (1981), 638-652.

MsSrWa1980 B. Marshall, W. Strauss, S. Wainger, L^p -> L^q estimates for the Klein-Gordon equation, J. Math. Pure Appl. 59 (1980), 417-440.

Mt-p Y. Martel, Multi-soliton-type solutions of the generalized KdV equations, preprint

• frank.dvi MtMe-p Y. Martel, F. Merle, [frank.dvi A Liouville theorem for the critical generalized Korteweg-de Vries equation], preprint.

MtMe2001 Y. Martel, F. Merle, Instability of solitons for the critical generalized Korteweg de Vries equation, GAFA 11 (2001), 74-123.

MtMe2002 Y. Martel, F. Merle, Nonexistence of blow-up solution with minimal L^2 mass for the critical gKdV, DMJ 115 (2002), 385-408.

MtMe-p3 Y. Martel, F. Merle, Asymptotic stability of solitons for the subcritical generalized Korteweg de Vries equations, preprint.

MtMe-p4 Y. Martel, F. Merle, Stability of the blowup profile and lower bounds for blowup rate for the critical generalized KdV equation, preprint.

MtMe-p Y. Martel, F. Merle, Asymptotic stability of solitons for the subcritical generalized Korteweg de Vries equations revisited, preprint.

MtMeTsa-p Y. Martel, F. Merle, T-P. Tsai, [arXiv.org/abs/math.AP/0112071 Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations], preprint

MasNa2002 N. Masmoudi, K. Nakanishi, From non-linear Klein-Gordon equation to a system of coupled Schrodinger equations, Math Ann. 324 (2002) 2, 359-389

MasNa2003 N. Masmoudi, K. Nakanishi, Nonrelativistic limit from Maxwell-Klein-Gordon and Maxwell-Dirac to Poisson-Schrodinger, IMRN 2003:13

Mm1976 A. Matsumura, On the asymptotic behavior of solutions of semilinear wave equations, Publ. Res. Inst. Math. Sci. 12 (1976/1977), 169-189.

Max-p D. Maxwell, Rough solutions of the Einstein constraint equations, preprint

Max2005 D. Maxwell, Rough solutions of the Einstein constraint equations on compact manifolds, J. Hyp. Diff. Eq. 2 (2005), 521-546.

Me1992 F. Merle, Construction of solutions with exactly k blow-up points for the Schrodinger equation with critical non-linearity, Comm. Math. Phys. 149 (1992), 205-214.

Me1993 F. Merle, Determination of blow-up solutions with minimal mass for nonlinear Schrodinger equation with critical power, Duke Math. J. 69 (1993), 427-453.

Me1996 F. Merle, Asymptotics for L^2 minimal blowup solutions of critical nonlinear Schrodinger equation, Ann. Inst. Henri Poincare 13 (1996), 553-565.

Me1996b F. Merle, Lower bounds for the blowup rate of solutions to the Zakharov equation in dimension 2, Comm. Pure Appl. Math. 49 (1996), 765-794.

Me1998 F. Merle, Blow-up phenomena for critical nonlinear Schrodinger and Zakharov equations, Proc. Int. Cong. Mat. (Berlin 1998), Doc. Math. J. DMV.

Me2001 F. Merle, Existence of blow-up solutions in the energy space for the critical generalized KdV equation, J. Amer. Math. Soc. 14 (2001), 555-578.

MeRap-p F. Merle, P. Raphael, Blowup dynamic and upper bound on the blowup rate for the critical nonlinear Schrodinger equation, preprint.

MeRap-p2 F. Merle, P. Raphael, Sharp upper bound on the blowup rate for the critical nonlinear Schrodinger equation, GAFA 13 (2003), 591-642.

MeRap2004 F. Merle, P. Raphael, On universality of blowup profile for L^2 critical nonlinear Schrodinger equation, Invent. Math. 156 (2004), 565-672.

MeVe1998 F. Merle, L. Vega, Compactness at blow-up time for L^2 solutions of the critical nonlinear Schrodinger equation in 2D, IMRN 9 (1998), 399-425.

MeVe2003 F. Merle, L. Vega, L^2 stability of solitons for the KdV equation, IMRN 2003:13.

MeZaa2003 F. Merle, H. Zaag, Determination of the blowup rate for the semilinear wave equation, AJM 125 (2003), 1147 - 1165

Met-p2 J. Metcalfe, Global existence for semilinear wave equations exterior to nontrapping obstacles, preprint.

MetSo-p J. Metcalfe, C.D. Sogge, Hyperbolic trapped rays and global existence of quasilinear wave equations, preprint.

MetSo-p2 J. Metcalfe, C.D. Sogge, Global existence for Dirichlet-wave equations with quadratic nonlinearties in high dimensions, preprint.

MetNkrSo-p J. Metcalfe, M. Nakamura, C. Sogge, Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains, preprint.

Mia1995 C. Miao, The global existence and asymptotic of solution for the Klein-Gordon-Schrodinger equations, Science in China, Ser. A, 38 (1995) 1444-1456.

Mia1997 C. Miao, H^m-modified wave operator for nonlinear Hartree equation in the dimensions space n \geq 2, Acta Math. Sinica 15 (1997), 247-268.

Mia1998 C. Miao, On space-time means and solutions to a class of nonlinear parabolic equations, Science in China, 42 (1998) 682-693.

Mia1999 C. Miao, The well-posedness of Cauchy problem for the coupled system of Schrodinger-KdV equations, Acta. Math. Sinica, 15 (1999), 215-224.

MiaZgFg-p C. Miao, B. Zhang, D. Fang, Global well-posedness for the Klein-Gordon equation below the energy norm, preprint.

MiaZg-p1 C. Miao, B. Zhang, Besov spaces and self-similar solutions for nonlinear evolution equations, preprint.

MiaZgZgx-p C. Miao, B. Zhang, X. Zhang, Self-similar solutions for nonlinear Schrodinger equations, preprint.

MiaZgZgx-p2 C. Miao, B. Zhang, X. Zhang, A note on self-similar solutions of the Schrodinger equation, preprint.

Mi1976 R. Miura, The Korteweg-de Vries equation: A survey of results, SIAM Review 18 (1976), 412-459.

MiGarKru1968 R. Miura, C. Gardner, M. Kruskal, Korteweg-de Vries equation and generalizations II. Existence of conservation laws and constant of motion, JMP 9 (1968), 1204-1209.

Mzh1985 S. Mizohata, On the Cauchy problem, Notes and Reports in Math and Science and Engineering, Science Press & Academic Press 3 (1985).

Miz2001 T. Mizumachi, Large Time Asymptotics of Solutions Around Solitary Waves to the Generalized Korteweg-de Vries Equations, SIAM Journal on Mathematical Analysis Volume 32, Number 5 (2001) pp. 1050-1080

Ml1999 L. Molinet, On the asymptotic behavior of solutions to the (generalized) Kadomtsev-Petviashvili-Burgers equations, JDE 152 (1999), 30-74.

MlRi-p L. Molinet, F. Ribaud, Well-posedness results for the Benjamin-Ono equation with small initial data, preprint.

MlRi2001 L. Molinet, F. Ribaud, The Cauchy problem for dissipative Korteweg-de Vries equations in Sobolev spaces of negative order, IUMJ 50(4) (2001), 1745-1776.

MlSauTz2001 L. Molinet, J.-C. Saut, N. Tzvetkov, Ill-posedness issues for the Benjamin-Ono and related equations, SIAM J. Math. Anal. 33 (2001), 982--988.

MlSauTz-p2 L. Molinet, J.-C. Saut, N. Tzvetkov, Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation, Duke Math J. 115 (2002), 352-384.

MlSauTz-p3 L. Molinet, J.-C. Saut, N. Tzvetkov, Global well-posedness for the Kadomtsev-Petviashvili-I equation, Math Annalen 324 (2002), 255-275.Errata, to appear, Math. Annalen.

Mc1980 V. Moncrief, Global existence of Maxwell-Klein-Gordon fields in (2+1)-dimensional spacetime, J. Math. Phys. 21 (1980), 2291-2296.

Mo1998 S.J. Montgomery-Smith, Time Decay for the Bounded Mean Oscillation of Solutions of the Schrodinger and Wave Equation, Duke Math J. 19 (1998), 393-408.

Mz1961 C.S. Morawetz, The decay of solutions to the exterior initial-boundary problem for the wave equation, CPAM 14(1961), 561-568.

Mz1966 C.S. Morawetz, Exponential decay of solutions to the wave equation, Comm. Pure and Appl. Math. 19 (1966), 439-444.

Mz1968 C.S. Morawetz, Time decay for the non-linear Klein-Gordon equation, Proc. Roy. Soc. A 306 (1968), 291-296.

Mz1975 C.S. Morawetz, Decay for solutions of the exterior problem for the wave equation, CPAM 28 (1975), 229-264.

MzRalSr1977 C.S. Morawetz, J. Ralston, W. Strauss, Decay of solutions of the wave equation outside of convex obstacles, CPAM 30 (1977), 447-508.

Mr1997 K. Moriyama, Normal' forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension, DIE 10 (1997) 499-520.

MrTwTs1997 K. Moriyama, S. Tonegawa, Y. Tsutsumi, Almost global existence of solutions for the quadratic semilinear Klein-Gordon equation in one space dimension. Funkcial. Ekvac. 40 (1997), 313-333

MyVaVg1996 A. Moyua, A. Vargas, L. Vega, Schrodinger Maximal Function and Restriction Properties of the Fourier transform, International Math. Research Notices 16 (1996).

MuSw1996 S. Muller, M. Struwe, Global existence of wave maps in 1+2 dimensions with finite energy data. Topol. Methods Nonlinear Anal. 8 (1996), 245-259.

MurTao-p T. Muramatu, S. Taoka, The initial value problem for the 1-D semilinear Schrodinger equation in Besov spaces, preprint.

N

NdStvUh2003 A. Nahmod, A. Stefanov, K. Uhlenbeck, On Schrodinger maps, CPAM 56 (2003), 114-151

NdStvUh2003b A. Nahmod, A. Stefanov, K. Uhlenbeck, On the well-posedness of the wave map problem in high dimensions, Comm. Anal. Geom. 11 (2003), 49-83.

Nj1990 B. Najman, The nonrelativistic limit of the nonlinear Klein-Gordon equation, Nonlinear Anal. 15 (1990), 217-228.

NkTs1986 K. Nakamitsu, Y. Tsutsumi, The Cauchy problem for the coupled Maxwell-Schrodinger equations, JMP 27 (1983), 211-216.

NkrOz1997 M. Nakamura, T. Ozawa, Low energy scattering for nonlinear Schrodinger equations in fractional order Sobolev spaces, Rev. Math. Phys. 9 (1997), 397-410.

NkrOz1998 M. Nakamura, T. Ozawa, Nonlinear Schrodinger equations in the Sobolev space of critical order, JFA 155 (1998) 364-380.

NkrOz-p M. Nakamura, T. Ozawa, Small solutions to nonlinear Schrodinger and Klein-Gordon equations, preprint.

NkrWad-p M. Nakamura, T. Wada, Local well-posedness for the Maxwell-Schrodinger equation, preprint.

Na1999 K. Nakanishi, Local well-posedness and Illposedness in the critical Besov spaces for semilinear wave equations with quadratic forms, Funk. Ekvac. 42 (1999), 261-279.

Na1999b K. Nakanishi, Unique global existence and asymptotic behaviour of solutions for wave equations with non-coercive critical nonlinearity, Comm. Partial Differential Equations. 24 (1999), 185-221.

Na1999c K. Nakanishi, Energy scattering for non-linear Klein-Gordon and Schrodinger equations in spatial dimensions 1 and 2, JFA 169 (1999), 201-225.

Na1999d K. Nakanishi, Scattering Theory for Nonlinear Klein-Gordon Equation with Sobolev Critical Power, IMRN 1999, 31-60.

Na1999e K. Nakanishi, Energy Scattering for Hartree equations, MRL 6 (1999), 107-118.

Na-p K. Nakanishi, Nonrelativistic limit of scattering theory for nonlinear Klein-Gordon equations, preprint.

Na2001 K. Nakanishi, Asymptotically free solutions for short range nonlinear Schrodinger equation, SIAM J. Math Anal. 32 (2001), 1265-1271.

Na-p3 K. Nakanishi, Modified wave operators for the Hartree equation with data, image, and convergence in the same space, preprint.

Na-p4 K. Nakanishi, Modified wave operators for the Hartree equation with data, image, and convergence in the same space II, preprint.

Na-p5 K. Nakanishi, Remarks on the energy scattering for nonlinear Klein-Gordon and Schrodinger equations, preprint.

NaOz2002 K. Nakanishi, T. Ozawa, Remarks on small data scattering for nonlinear Schrodinger equations, Nonlinear Diff. Eq. and Appl. 9 (2002), 45-68.

NaOz-p K. Nakanishi, T. Ozawa, Global solutions for nonlinear Schrodinger equations with arbitrarily growing nonlinearity and contracted initial data, preprint.

NaTkTs2001 K. Nakanishi, H. Takaoka, Y. Tsutsumi, Counterexamples to bilinear estimates related with the KdV equation and the nonlinear Schrodinger equation, Methods and Applications of Analysis 8 (2001), 569-578.

Nk2001 M. Nakao, L^p estimates for the wave equation and global existence for semilinear wave equations in exterior domains, Math. Annalen 320 (2001), 11-31.

NwOz1992 H. Nawa, T. Ozawa, Nonlinear scattering with nonlocal interaction, Comm. Math. Phys. 146 (1992), 259-275.

Nw1990 H. Nawa, Convergence theorems for the pseudo-conformally invariant nonlinear Schrödinger equation. Proc. Japan Acad. Ser. A Math. Sci. 66 (1990), no. 7, 214--216.

Nw1991 H. Nawa, Formation of singularities in solutions of the nonlinear Schrödinger equation. Proc. Japan Acad. Ser. A Math. Sci. 67 (1991), no. 1, 29--34.

Nw1992 H. Nawa, \u201cMass concentration" phenomenon for the nonlinear Schrödinger equation with the critical power nonlinearity. Funkcial. Ekvac. 35 (1992), no. 1, 1--18.

Nw1994 H. Nawa, Asymptotic profiles of blowup solutions to the nonlinear Schrodinger equation with critical power nonlinearity, J. Math. Soc. Japan 46 (1994), no. 4, 557--586.

Nw1997 H. Nawa, Limiting profiles of blowup solutions of the nonlinear Schrodinger equation with critical power nonlinearity, Proc. Japan Acad. Ser. A Math Sci. 73 (1997), 171-175.

Nw1998 H. Nawa, Two points blow up in solutions to the nonlinear Schrodinger equation with quartic potential on R, J. Stat. Phys. 91 (1998), 439-458.

Nw1999 H. Nawa, Asymptotic and limiting profiles of blowup solutions of the nonlinear Schrodinger equation with critical power, CPAM52 (1999), 193-270.

NwTs1989 H. Nawa, Y. Tsutsumi, On blow-up for the pseudo-conformally invariant nonlinear Schrödinger equation. Funkcial. Ekvac. 32 (1989), no. 3, 417--428.

NwTs1998 H. Nawa, Y. Tsutsumi, On blowup for the conformally invariant nonlinear Schrodinger equation II, CPAM 51 (1998), 373-383.

Nm1997 P.I. Naumkin, Asymptotics for large time for nonlinear Schrodinger equation, Nonlinear waves (Sapporo, 1995), 367-373, GAKUTO Internat. Ser. Math. Sci. Appl., 10, Gakk\=otosho, Tokyo, 1997.

Nm1997b P.I. Naumkin, Asymptotic behavior for large time values of solutions of the nonlinear Schrödinger equation. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 61 (1997), no. 4, 81-118; translation in Izv. Math. 61 (1997), no. 4, 757-794.

Nic1996 J.P. Nicolas, Nonlinear Klein-Gordon equation on Schwarzschild-like metrics, J. Math. Pures Appl. (9) 74 (1995), 35-58.

NieSf2003 F. Nier, A. Soffer, Dispersion and Strichartz estimates for some finite rank perturbations of the Laplace operator, JFA 198 (2003), 511-535

No1980 V. J. Novoksenov, Asymptotic behaviour as $t \to \infty$ of the solution to the Cauchy problem for a nonlinear Schr\"odinger equation (Russian), Dokl. Akad. Nauk SSSR 251 (1980), 799-802.

O

Ob1989 D. Oberlin, Convolution estimates for some distributions with singularities on the light cone, Duke Math J. 59 (1989), 747-757.

OgOz1991 T. Ogawa, T. Ozawa, Trudinger type inequalities and uniqueness of weak solutions for the nonlinear Schrodinger equation, JMAA 155 (1991) 531-540.

OgTs1989 T. Ogawa, Y. Tsutsumi, Blowup solutions for the nonlinear Schrodinger equation with quartic potential and periodic boundary conditions, LNM 1450 (1989), 236-261.

OgTs1991 T. Ogawa, Y. Tsutsumi, Blow-up of H^1 solution for the nonlinear Schrödinger equation. J. Differential Equations 92 (1991), no. 2, 317-330.

Oh1989 Y-G. Oh, Cauchy's problem and Ehrenfest's law for nonlinear Schrodinger equations with potentials, JDE 81 (1989), 255-274.

On1975 H. Ono, Algebraic solitary waves in stratified fluids, J. Phys.Soc. Japan 39 (1975), 1082-1091.

OttSud1970 E. Ott, N. Sudan, Damping of solitary waves, Phys. Fluids 13(6) (1970), 1432-1434.

Oz1991 T. Ozawa, Long range scattering for nonlinear Schrodinger equations in one space dimension, CMP 139 (1991), 479-493

Oz1995 T. Ozawa, Remarks on quadratic nonlinear Schrodinger equations, Funkcial. Ekvac. 38 (1995), 217-232.

Oz1996 T. Ozawa, On the nonlinear Schrodinger equations of derivative type, Indiana Univ. Math. J. 45 (1996), 137-163.

OzTs1992 T. Ozawa, Y. Tsutsumi, Existence and smoothing effect of solutions for the Zakharov equations, RIMS. Kyoto U. 28 (1992), 329-361.

OzTs1992b T. Ozawa, Y. Tsutsumi, The nonlinear Schrodinger limit and the initial layer of the Zakharov equations, Diff. Int. Eq. 5 (1992) 721-745.

OzTs1994 T. Ozawa, Y. Tsutsumi, Global existence and asymptotic behavior of solutions for the Zakharov equations in three space dimensions. Adv. Math. Sci. Appl. 3 (1993/94), Special Issue, 301-334.

OzTs1994b . T. Ozawa, Y. Tsutsumi, Asymptotic behaviour of solutions for the coupled Klein-Gordon-Schrodinger equations, in Spectral and Scattering theory and Applications, Adv. Stud. in Pure Math, Jap. Math. Soc. 23 (1994), 295-305.

OzTs1998 T. Ozawa, Y. Tsutsumi, Space-time estimates for null gauge forms and nonlinear Schrödinger equations. Differential Integral Equations 11 (1998), 201-222

OzTyTs1995 T. Ozawa, K. Tsutaya, Y. Tsutsumi, Normal' form and global solutions for the Klein-Gordon-Zakharov equations. Ann. Inst. H. Poincare Anal. Non Lineaire 12 (1995), 459-503.

OzTyTs1996 T. Ozawa, K. Tsutaya, Y. Tsutsumi, Global existence and asymptotic behavior of solutions for the Klein-Gordon equation with quadratic non-linearity in two space dimensions, Math. Z. 222 (1996), 341-362.

OzTyTs1997 T. Ozawa, K. Tsutaya, Y. Tsutsumi, Remarks on the Klein-Gordon equation with quadratic nonlinearity in two space dimensions. Nonlinear waves (Sapporo, 1995), 383-392, GAKUTO Internat. Ser. Math. Sci. Appl., 10, Gakkotosho, Tokyo, 1997.

OzTyTs1999 T. Ozawa, K. Tsutaya, Y. Tsutsumi, Well-posedness in energy space for the Cauchy problem of Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions, Math. Annalen. 313 (1999), 127-144.

OzTyTs2000 T. Ozawa, K. Tsutaya, Y. Tsutsumi, On the coupled system of nonlinear wave equations with different propagation speeds, Proc. Conf. "Evolution Equations: Existence, Regularity and Singularities", Banach Center publications 52, Warsawa 2000

P

PaWghWgy2000 P. Pang, H. Wang, Y.D. Wang, Local existence for inhomogeneous Schrodigner flow of maps into Kahler manifolds, Acta Math. Sinica 16 (2000), 487.

PaWghWgy-p P. Pang, H. Wang, Y.D. Wang, Schrodinger flow of maps into Kahler manifolds, Asian J. Math, preprint.

Pe1982 H. Pecher, Decay of solutions of nonlinear wave equations in three space dimensions, J. Funct. Anal. 46 (1982), 221-229.

Pe1984 H. Pecher, Nonlinear small data scattering for the wave and Klein-Gordon equations, Math. Z. 185 (1984), 261-270.

Pe1985 H. Pecher, Low energy scattering for nonlinear Klein-Gordon equations, J. Funct. Anal. 63 (1985), 101-122.

Pe-p2 H. Pecher, Global solutions of the Klein-Gordon-Schrodinger system with rough data, preprint.

PgWs1992 R. Pego, M. Weinstein, Eigenvalues, and instability of solitary waves, Phil. Trans. R. Soc. London A 340 (1992), 47-94.

PgWs1994 R. Pego, M. Weinstein, Asymptotic stability of solitary waves, CMP 164 (1994), 305-349.

Pn1964 R. Penrose, Conformal treatment of infinity, Relativite, Groupes et Topologie, Gordon and Breach NY (1964), 565-584.

Pn1965 R. Penrose, Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14 (1965) 57-59.

Per1997 G. Perelman, Some results on the scattering of weakly interacting solitions for nonlinear Schrodinger equations, in \u201cSpectral theory, microlocal analysis, singular manifolds\u201d, Akad. Verlag (1997), 78\u2014137.

Per-p G. Perelman, On the blow up phenomenon for the critical nonlinear Schrodinger equation in 1D, preprint.

PvYn1989 V. Petviashvili, V. Yan'kov, Solitons and turbulence, in B. B. Kadomtsev (ed.) Rev. Plasma Physics XIV (1989), 1-62

PiWn1997 C.A. Pillet, C.E. Wayne, Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations, JDE 141 (1997), 310-326.

Pl2000 F. Planchon, On the Cauchy problem in Besov spaces for a nonlinear Schrodinger equation, Commun. Contemp. Math. 2 (2000), 243-254.

Pl2002 F. Planchon, Remarks on Strichartz estimates on null forms, DIE 15 (2002), 697-708

Pl-p F. Planchon, Dispersive estimates and the 2D cubic NLS equation, preprint.

Pl-p2 F. Planchon, On self-similar solutions, well-posedness, and the conformal wave equation, preprint.

Pl-p4 F. Planchon, Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations, Proc. Journees EDP, St Jean de Monts, 1999.

Pl-p5 F. Planchon, On uniqueness for semilinear wave equations, preprint.

PlStaTv2003 F. Planchon, J. Stalker, A. Shadi Tahvidar-Zadeh, L^p estimates for the Wave Equation with the Inverse-Square Potential, Discrete Contin. Dynam. Systems. 9(2003) 427\u2014442.

Pm1976 K. Pohlmeyer, Integrable Hamiltonian systems and interaction through quadratic constraints, Comm. Math. Phys., 46 (1976), 207-221.

Po1989 G. Ponce, Regularity of solutions to nonlinear dispersive equations, J. Diff. Eq. 78 (1989), 122-135.

Po1991 G. Ponce, On the global well-posedness of the Benjamin-Ono equation, DIE 4 (1991), 527-542.

PoSi1993 G. Ponce, T. Sideris, Local regularity of nonlinear wave equations in three space dimensions, CPDE 18 (1983), 169-177.

PoVe1990 G. Ponce, L. Vega, Non-linear small data scattering for the generalized Korteweg-de Vries equation, J. Funct. Anal. 90 (1990), 445-457.

Pop2001 M. Poppenberg, On the local well posedness of quasilinear Schrödinger equations in arbitrary space dimension. J. Differential Equations 172 (2001), no. 1, 83--115.

Pop2001b M. Poppenberg, Smooth solutions for a class of fully nonlinear Schrödinger type equations. Nonlinear Anal. 45 (2001), no. 6, Ser. A: Theory Methods, 723--741.

Q
R

Ral1969 J. Ralston, Solutions of the wave equation with localized energy, CPAM 22(1969), 807-923.

Rm1987 M. Rammaha, Finite-time blowup for nonlinear wave equations in high dimensions, CPDE 12 (1987), 677-700

Rap-p P. Raphael, Stability of the log-log bound for blowup solutions to the critical nonlinear Schrodinger equation, preprint.

Ra1978 J. Rauch, Local decay of scattering solutions to Schrodinger's equation, CMP 61 (1978), 149-168.

Ra1981 J. Rauch, The u^5 Klein-Gordon equation II. Anomalous singularities for semilinear wave equations, in H. Brezis and P. Lions, editors, Nonlinear Partial Differential Equations and Their Applications, Research Not. in Math. 53 Pittman (1981), 335-364.

RaRe1982 J. Rauch, M. Reed, Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension, Duke Math. J., 49

RaySt-p S. Raynor, G. Staffilani, Stability of solitons for the KdV equation in H^s, 0 <= s < 1, preprint.

Re1987 M. Reed, Abstract Nonlinear Wave Equations, Lecture Notes in Mathematics 507, Springer-Verlag, New York 1976.

Rei1990 G. Rein, Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics, CMP 135 (1990), 41-78.

Ren2002 A. Rendall, Theorems on existence and global dynamics for the Einstein equations. Living Reviews in Relativity 5, 6 (2002). gr-qc/0203012.

RenFri2000 A. Rendall and H. Friedrich, The Cauchy problem for the Einstein equations. In B. G. Schmidt (ed) Einstein's Field Equations and Their Physical Implications. Lecture Notes in Physics 540. Springer, Berlin (2000). gr-qc/0002074

RiYou1998 F. Ribaud, A. Youssfi, Regular and self-similar solutions of nonlinear Schrodinger equations, J. Math. Pure Appl. 77 (1998), 1065-1079

RoScg-p I. Rodnianski, W. Schlag, Time decay for solutions of Schrodinger equations with rough and time-dependent potentials, preprint.

RoScgSf-p I. Rodnianski, W. Schlag, A. Soffer, Dispersive analysis of charge transfer models, preprint.

RoScgSf-p2 I. Rodnianski, W. Schlag, A. Soffer, Asymptotic stability of N-soliton states of NLS, preprint.

RoTa-p I. Rodnianski, T. Tao, Global regularity for the Maxwell-Klein-Gordon equation in high dimensions, preprint.

RsWs1988 H. Rose, M. Weinstein, On the bound states of the nonlinear Schrodinger equation with a linear potential, Physica D 30 (1998), 207-218

RuVe1993 A. Ruiz, L. Vega, On local regularity of Schrodinger equations, IMRN 1993 (1993), 13-27.

RuVe1994 A. Ruiz, L. Vega, Local regularity of solutions to wave with time dependent potentials, Duke Math J. 76 (1994), 913-940.

S

Sau1979 J.C. Saut, Sur quelques generalizations de l'equation de Korteweg-de Vries, J. Math. Pures Appl. 58 (1979), 21-61.

Sau1993 J.C. Saut, Remarks on the generalized Kadomtsev-Petviashvili equations, Indiana U. Math. J. 42 (1993), 1017-1029.

Sau1995 J.C. Saut, Recent results on the generalized Kadontsev-Petviashvili equations, Acta Appl. Math. 39 (1995), 477-487.

SauSc1987 J.-C. Saut, B. Scheurer, Unique continuation for some evolution equations, J. Diff. Eq. 66 (1987), 118-139.

SauTem1976 J.C. Saut, R. Temam, Remarks on the Korteweg-de Vries equation, Israel J. Math. 24 (1976), 78-87.

SauTz1999 J.C. Saut, N. Tzvetkov, The Cauchy problem for higher order KP equations, J. Diff. Eq. 153 (1999), 192-222.

SauTz2000 J.C. Saut, N. Tzvetkov, The Cauchy problem for the fifth order KP equations, J. Math. Pures Appl. (2000), 307-338.

SauTz-p J.C. Saut, N. Tzvetkov, On periodic KP-I type equations, preprint.

Scf1985 J. Schaeffer, The equation Box u = |u|^p fror the critical value of p, Proc. Roy. Soc. Edinburgh 101A (1985), 31-44.

Scf1986 J. Schaeffer, The classical limit of the relativistic Vlasov-Maxwell system, CMP 104 (1986), 409-421.

Sch1998 G. Schneider, Approximation of the Korteweg-de Vries equation by the nonlinear Schr\"odinger equation, J. Differential Equations 147 (1998), 333-354.

Scr1986 P. Schuur, Asymptotic analysis of soliton problems, LNM 1232 (1986), Springer-Verlag, Berlin

SctWs1986 S. Schochet, M. Weinstein, The nonlinear Schrodinger limit of the Zakharov equations governing Langmuir turbulence, Comm. Math. Phys. 106 (1986), 569-580.

Scz1987 M. Schwarz Jr., Periodic solutions of Kadomtsev-Petviashvili, Adv. Math. 66 (1987) 217-233.

Sg1976 I.E. Segal, Space-time Decay for Solutions of Wave Equations, Adv. Math., 22 (1976), 304-311.

SeAb1976 H. Segur, M. Ablowitz, Asymptotic solutions and conservation laws for the nonlinear Schr\"odinger equation I. J. Math. Phys. 17 (1976), 710-713.

Sb-p S. Selberg, Multilinear space-time estimates and applications to local existence theory for non-linear wave equations, Princeton University Thesis.

Sb-p2 S. Selberg, Some remarks on well-posedness of nonlinear wave equations, preprint.

Sb-p3 S. Selberg, Wave maps and bilinear spacetime estimates, preprint.

Sb-p4 S. Selberg, On an estimate for the wave equation and applications to non-linear problems, preprint.

Sb-p5 S. Selberg, Almost optimal local well-posedness of the Maxwell-Klein-Gordon equations on $\R^{1+4}$, preprint.

Sa1982 J. Shatah, Global existence of small solutions to nonlinear wave equations, JDE 46 (1982), 409-425.

Sa1983 J. Shatah, Unstable ground state of nonlinear Klein Gordon equations, Trans. Amer. Math. Soc. 290 (1985), 701-710.

Sa1985 J. Shatah, Normal forms and quadratic non-linear Klein-Gordon equations, Comm. Pure. Appl. Math. 38 (1985), 685-696.

Sa1988 J. Shatah, Weak solutions and development of singularities of the SU(2) sigma-model, Comm. Pure Appl. Math., 41 (1988), 459-469.

Sa1988b J. Shatah, Recent advances in nonlinear wave equations. Dynamical problems in continuum physics (Minneapolis, Minn., 1985), 305-309, IMA Vol. Math. Appl., 4, Springer, New York-Berlin, 1987

Sa1994 J. Shatah, The Cauchy problem for harmonic maps on Minkowski space, in Proceed. Inter. Congress of Math. 1994, Birkh\"auser, 1126-1132.

Sa1994b J. Shatah, Geometric wave equations, Recent advances in partial differential equations (El Escorial, 1992), 99-114, RAM Res. Appl. Math., 30, Masson, Paris, 1994.

Sa1997 J. Shatah, Regularity results for semilinear and geometric wave equations, Mathematics of gravitation, Part I (Warsaw, 1996), 69-90, Banach Center Publ., 41, Part I, Polish Acad. Sci., Warsaw, 1997.

SaTv1992 J. Shatah, A. Tavildar-Zadeh, Regularity of harmonic maps from the Minkowski space into rotationally symmetric manifolds. Comm. Pure Appl. Math. 45 (1992), 947-971.

SaTv1994 J. Shatah, A. Tavildar-Zadeh, On the Cauchy problem for equivariant wave maps, Comm. Pure Appl. Math., 47 (1994), 719 - 753.

SaTv1997 J. Shatah, A. Tavildar-Zadeh, On the stability of stationary wave maps, Comm. Math. Phys. 185 (1997), no. 1, 231-256.

J. Shatah, W. Strauss, Instability of nonlinear bound states. Comm. Math. Phys. 100 (1985),  173-190.


SaSr1996 J. Shatah, W. Strauss, Breathers as homoclinic geometric wave maps, Physics D 99 (1996), 113-133.

SaSw1993 J. Shatah, M. Struwe, Regularity results for non-linear wave equations, Ann. of Math. 138 (1993) 503-518.

SaSw1994 J. Shatah, M. Struwe, Well Posedness in the energy space for semilinear wave equations with critical growth, Inter. Math. Research Not., 7 (1994).

SaSw1998 J. Shatah, M. Struwe, Geometric wave equations, Courant Lecture Notes in Mathematics 2 (1998)

SaSw2001 J. Shatah, M. Struwe, The Cauchy problem for wave maps, IMRN 2002:11 (2002) 555-571

ShbTs1984 Y. Shibata, Y. Tsutsumi, Global existence theorem for nonlinear wave equation in exterior domains, Recent topics in nonlinear PDE (Hiroshima 1983), North-Holland Math. Stud., NY 98 (1984) 155-196.

ShbTs1986 Y. Shibata, Y. Tsutsumi, On a global existence theorem of small-amplitude solutions for nonlinear wave equations in an exterior domain, Math Z. 191 (1986), 165-199.

ShbTs1987 Y. Shibata, Y. Tsutsumi, Local existence of solution for the initial-boundary value problem of fully nonlinear wave equation, Nonlinear Anal. 11 (1987), 335-365.

ShiTon2004 A. Shimomura, S. Tonegawa, Long range scattering for nonlinear Schrodinger equations in one and two space dimensions, DIE 17 (2004), 127-150.

Shu1991 W-T. Shu, Asymptotic properties of solutions of the linear and nonlinear spin field equations in Minkowski space, CMP 140 (1991), 449-480.

Si1981 T. Sideris, Ph.D. Thesis, Bloomington Indiana U. 1981.

Si1983 T. Sideris, Global behavior of solutions to nonlinear wave equations in three space dmensions, CPDE 8 (1983), 1291-1323.

Si1984 T. Sideris, Non-existence of global solutions to semilinear wave equations in high dimensions, J. Diff. Eq. 52 (1984), 378-406.

Si1989 T. Sideris, Global existence of harmonic maps in Minkowski space, Comm. Pure Appl. Math., 42 (1989),1-13.

Si1996 T. Sideris, The null condition and global existence of nonlinear elastic waves, Invent. Math. 123 (1996), 323-342.

Si2000 T. Sideris, Nonresonance and global existence of prestressed nonlinear elastic waves, Annals. of Math. 151 (2000), 849-874.

SiTu-p T. Sideris, S. Tu, Global existence for systems of nonlinear wave equations in 3D with multiple speeds, preprint.

SidSucSup1986 A. Sidi, C. Sulem, P.-L. Sulem, On the long-time behavior of a generalized KdV equation, Acta Applicandae Math. J. 7 (1986), 35-47.

SnTl1985 J. Simon, E. Taflin, Wave operators and analytic solutions for systems of nonlinear Klein-Gordon equations and of nonlinear Schrodinger equations, CMP 99 (1985), 541-562.

SnTl1993 J. Simon, E. Taflin, The Cauchy problem for non-linear Klein-Gordon equation and applications, Comm. Math. Phys. 152 (1993), 433-478.

Sj1970 A. Sjoberg, On the Korteweg-de Vries equation: Existence and uniqueness, J. Math. Anal. Appl. 29 (1970), 569-579.

Sl1987 P. Sjolin, Regularity of solutions to the Schrodinger equation, Duke Math. J. 55 (1987), 699-715.

Smh1992 H. Smith, A parametrix construction for wave equation with C^{1,1} coefficients, Ann. d'Institut Fourier 48 (1998), 797 - 835.

Smh-p H. Smith, Small data scattering for a nonlinearly damped wave equation, preprint.

SmhSo1994 H. Smith, C.D. Sogge, L^p regularity for the wave equation with strictly convex obstacles, Duke Math. J. 73(1994), 97-155.

SmhSo1995 H. Smith, C.D. Sogge, On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc. (1995), 879-916.

SmhSo-p H. Smith, C.D. Sogge, Global Strichartz estimates for nontrapping perturbations of the Laplacian, CPDE 25 (2000), 2171-2183.

SmhSo-p2 H. Smith, C.D. Sogge, Null form estimates for (1/2,1/2) symbols and local existence for a quasilinear Dirichlet-wave equation, preprint.

SmhTt-p H. Smith, D. Tataru, Sharp local well-posedness results for the nonlinear wave equation, preprint.

SmhTt-p2 H. Smith, D. Tataru, Counterexamples to Strichartz estimates for the wave equation with nonsmooth coefficients, preprint.

Smo1983 J. Smoller, Shock waves and reaction diffusion equations, Springer Verlag 1983

SfWs1990 A. Soffer, M. Weinstein, Multichannel nonlinear Scattering for nonintegrable equations, CMP 133 (1990), 119-146.

SfWs1999 A. Soffer, M. Weinstein, Resonances, radiation damping, and instability in Hamiltonian nonlinear wave equations, Invent. Math. 136 (1999), 9-74.

SfWs-p A. Soffer, M. Weinstein, Selection of the ground state for nonlinear Schrodinger equations, preprint.

So1993 C.D. Sogge, On local existence for nonlinear wave equations satisfying variable co-efficient null conditions, CPDE 18 (1993) 1795-1821.

So1995 C.D. Sogge, Lectures on Nonlinear Wave Equations, Monographs in Analysis II, International Press, 1995.

So2001 C.D. Sogge, Global existence for nonlinear wave equations with multiple speeds, Harmonic Analysis at Mount Holyoke (2001), 353-366, W. Beckner, A. Nagel, A. Seeger, H. Smith editors, AMS.

So-p C.D. Sogge, Estimates for the Dirichlet-wave equation and applications to nonlinear wave equations, preprint.

Sy1992 A. Souyer, The Cauchy problem for the Ishimori equations, JFA 105 (1992), 233-255.

SpMk-p C. Sparber, P. Markowich, Semiclassical asymptotics for the Maxwell-Dirac system, preprint.

St1995 G. Staffilani, University of Chicago Thesis.

St1997 G. Staffilani, Quadratic forms for a 2D semilinear Schrodinger equation, Duke Math J. 86 (1997), 79-107.

St1997b G. Staffilani, On the growth of high Sobolev norms of solutions for KdV and Schrodinger equations, Duke Math J. 86 (1997), 109-142.

St1997c G. Staffilani, On solutions for periodic generalized KdV equations,IMRN 18 (1997), 899-917.

St1997d G. Staffilani, On the generalized KdV equations, DIE 10 (1997), 777-796.

St2001 G. Staffilani, KdV and almost conservation laws, Harmonic Analysis at Mount Holyoke (2001), 367-382, W. Beckner, A. Nagel, A. Seeger, H. Smith editors, AMS.

StTt-p G. Staffilani, D. Tataru, Strichartz estimates for a Schrodinger operator with rough coefficients, preprint.

Stv-p A. Stefanov, Strichartz estimates for the Schrodinger equation with radial data, preprint.

Stz-p2 J. Sterbenz, Global Regularity and Scattering for General Non-Linear Wave Equations II. (4+1) Dimensional Yang--Mills Equations in the Lorentz Gauge, preprint

Stz-p3 J. Sterbenz, Global regularity and Scattering for general non-linear Wave Equations I. (6+1) and higher dimensions, preprint.

Stz-p4 J. Sterbenz, Angular regularity and Strichartz estimates for the wave equation, preprint.

Sr1968 W. Strauss, Decay and asymptotics for \Box u = F(u), J. Funct. Anal. 2 (1968), 409-457.

Sr1974 W. Strauss, Nonlinear scattering theory, Scattering theory in mathematical physics, J. Lavita, J.P. Marchand (eds), Riedel, Dordrecht (1974), 705-714.

Sr1975 W. Strauss, Dispersal of waves vanishing on the boundary of an exterior domain, CPAM 28 (1975), 265-278.

Sr1977 W. Strauss, Existence of solitary waves in higher dimensions, CMP 55 (1977), 149-162.

Sr1978 W. Strauss, Nonlinear invariant wave equations, Lecture notes in physics, Springer 78 (1978), 197-249.

Sr1981 W. Strauss, Non-linear scattering theory at low energy, J. Funct. Anal. 41 (1981), 110-133.

Sr1981b W. Strauss, Non-linear scattering theory at low energy: sequel, J. Funct. Anal. 43 (1981), 281-293.

Sr1981c W. Strauss, Dispersion of low-energy waves for two conservative equations, Arch. Rat. Mech. Anal. 55 (1974), 86-92.

Sr1989 W. Strauss, Nonlinear wave equations, Regional Conf. Series in Math., 1989.

SrVaz1986 W. Strauss, L. Vazquez, Stability under dilations of nonlinear spinor fields, Phys. Rev. D. (3) 34 (1986), 641-643.

Sz1977 R.S. Strichartz, Restriction of Fourier Transform to Quadratic Surfaces and Decay of Solutions of Wave Equations, Duke Math. J., 44 (1977), 705-713.

Sz1981 R.S. Strichartz, Asymptotic behavior of waves, J. Funct. Anal. 40 (1981), 341-357.

Sw1988 M. Struwe, Globally regular solutions to the u^5 Klein-Gordon equations, Ann. Scuola Norm. Sup. Pisa 15 (1988), 495-513.

Sw1992 M. Struwe, Semilinear wave equations, Bull. Amer. Math. Soc. 26 (1992), 53-85.

Sw1997 M. Struwe, Wave Maps, in Nonlinear Partial Differential Equations in Geometry and Physics, Prog. in Nonlin. Diff. Eq. and their Applic., 29, (1997), Birkhauser, 113-150.

Sw2002 M. Struwe, Radially symmetric wave maps from the (1+2)-dimensional Minkowski space to a sphere, Math Z. 242 (2002), 407-414.

Sw2003 M. Struwe, Radially symmetric wave maps from (1+2)-dimensional Minkowski space to general targets, Calc. Var. 16 (2003), 431-437.

Sw-p M. Struwe, Evolution problems in Geometry and Mathematical Physics, AMS Prospects in Math. (ed. H. Rossi), 83-101.

Sw-p2 M. Struwe, Equivariant wave maps in two space dimensions, preprint.

SucSup1979 C. Sulem, P. Sulem, Quelques resultats de regularite pour les equations de la turbulence de Langmuir, C. R. Acad. Sc. Paris. 289 Serie A (1979), 173-176.

SucSup1999 C. Sulem, P. Sulem, The nonlinear Schrodinger equation: Self-Focusing and Wave Collapse, Applied Mathematical Sciences 139, Springer-Verlag, New York.

SucSupBds1986 C. Sulem, P. Sulem, C. Bardos, On the continuous limit of a system of classical spins, CMP 107 (1986), 431-454.

T

Tk1999 H. Takaoka, Well-posedness for the Schrodinger equation with the derivative non-linearity, Adv. Diff. Eq. 4 (1999), 561-680.

Tk2000 H. Takaoka, Global well-posedness for the Kadomtsev-Petviashvili II equation, Discrete Cont. Dynam. Systems 6 (2000), 483-499.

Tk-p H. Takaoka, Global well-posedness for the Schrodinger equations with derivative non-linearity below energy, preprint.

Tk-p2 H. Takaoka, Well-posedness for the Kadomtsev-Petviashvili II equation, Adv. Diff. Eq., to appear.

Tk-p3 H. Takaoka, Well-posedness for the Zakharov system with the periodic boundary condition, Diff. Int. Eq. (1999).

Tk-p4 H. Takaoka, Well-posedness for the higher-order nonlinear Schrodinger equation, preprint (1996).

TkTz-p2 H. Takaoka, N. Tzvetkov, On 2D nonlinear Schrodinger equations with data on RxT, preprint.

TkTz-p3 H. Takaoka, N. Tzvetkov, On 2D dispersive models, preprint.

TkTz-p4 H. Takaoka, N. Tzvetkov, On the local regularity of Kadomtsev-Petviashvili-II equation, preprint.

Tak1992 J. Takeuchi, Le probleme de Cauchy pour certaines equations sur derivees partielles du type de Schrodinger VIII; symetrisations independantes du temps, C.R. Acad. Sci. Paris t315, Serie 1 (1992), 1055-1058.

Ta1999 T. Tao, Low regularity semi-linear wave equations, Comm. PDE 24 (1999), 599-630

Ta2000 T. Tao, Ill-posedness for one-dimensional wave maps at the critical regularity, Amer. J. Math.122 (2000), 451-463

Ta2000b T. Tao, Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation, Comm. PDE 25 (2000), 1471-1485

Ta-p T. Tao, Global well-posedness for the Benjamin-Ono equation in H^1(R), preprint.

Ta-p2 T. Tao, Multilinear weighted convolution of L^2 functions, and applications to nonlinear dispersive equations, submitted, Amer. J. Math.

Ta-p3 T. Tao, Local well-posedness of the Yang-Mills equation in the Temporal gauge below the energy norm, submitted, DIE.

Ta-p4 T. Tao, Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates, submitted, Math. Z.

Ta-p5 T. Tao, Global regularity of wave maps I. Small critical Sobolev norm in high dimension, IMRN7 (2001), 299-328.

Ta-p6 T. Tao, Global regularity of wave maps II. Small energy in two dimensions, to appear, Comm. Math. Phys.

Ta-p7 T. Tao, On the asymptotic behavior of large radial data for a focusing non-linear Schr\"odinger equation, preprint.

Ta-p8 T. Tao, Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrodinger equation for radial data, preprint.

TaVa2000 T. Tao, A. Vargas, A bilinear approach to cone multipliers I. Restriction estimates, GAFA10 (2000), 185-215

TaVa2000b T. Tao, A. Vargas, A bilinear approach to cone multipliers II. Applications, GAFA10 (2000), 216-258

Tar1995 S. Tarama, On the wellposed Cauchy problem for some dispersive equations, J. Math. Soc. Japan 47 (1995), 143-158.

Tar1997 S. Tarama, Remarks on L^2-wellposed Cauchy problem for some dispersive equations, J. Math. Kyoto Univ. 37 (1997), 757-765.

Tt1996 D. Tataru, On the X^{s,\theta} spaces and unique continuation for semilinear hyperbolic equations, CPDE 21 (1996).

Tt1998 D. Tataru, Local and global results for wave maps I, CPDE 23 (1998), 1781-1793.

Tt1999 D. Tataru, On the equation \Box u = |\nabla u|^2 in R^{5+1}, Math. Res. Letters 6 (1999), 469-485.

Tt2000 D. Tataru, Strichartz estimates for operators with non-smooth co-efficients and the non-linear wave equation, American Journal of Mathematics 122 (2000), 349-376.

Tt2001 D. Tataru, Strichartz estimates for second-order hyperbolic operators with nonsmooth coefficients II, AJM 123 (2001) 385-423.

Tt2001b D. Tataru, On global existence and scattering for the wave maps equation, AJM 123 (2001), 37-77.

Tt2001c D. Tataru, Null form estimates for second order hyperbolic operators with rough coefficients, Harmonic Analysis at Mount Holyoke (2001), 383-410, W. Beckner, A. Nagel, A. Seeger, H. Smith editors, AMS.

Tt2002 D. Tataru, Nonlinear wave equations, Proc. ICM 2002 III, 209-220

Tt-p D. Tataru, Strichartz estimates in hyperbolic space and global existence for the semilinear wave equation, TAMS 353 (2001), 785-807.

Tt-p2 D. Tataru, Rough solutions for the wave maps equation, preprint.

Tt-p5 D. Tataru, Strichartz estimates for second-order hyperbolic operators with nonsmooth coefficients III, preprint.

Tt-p6 D. Tataru, Null form estimates for second order operators with rough co-efficients, preprint.

Tay2000 M. Taylor, Tools for PDE: Pseudodifferential Operators, Paradifferential Operators, and Layer potentials, Math. Surveys and Monographs 81, AMS 2001

Tem1969 R. Temam, Sur un probleme nonlineaire, J. Math. Pures Appl. 48 (1969), 159-172.

TeUh-p C.L. Terng, K. Uhlenbeck, Schrodinger flows on Grassmannians, in Integrable Systems, Geometry and Topology, Somerville MA: International Press.

TeUh-p2 C.L. Terng, K. Uhlenbeck, 1+1 wave maps into symmetric spaces, preprint.

Tom1990 M.M. Tom, Smoothing properties of some weak solutions of the Benjamin-Ono equation, DIE 3 (1990) 683-694.

Tom1996 M. M. Tom, On a generalized Kadomtsev-Petviashvili equation, Comteporary Mathematics AMS, 200 (1996), 193-210.

Tsa2003 T.P. Tsai, Asymptotic dynamics of nonlinear Schrodinger equations with many bound states, JDE 192 (2003), 225-282.

TsaYau2002 T.P. Tsai, H.T. Yau, Asymptotic dynamics of nonlinear Schrodinger equations: resonance dominated and dispersion dominated solutions, CPAM 55 (2002), 153-216.

TsaYau2002b T.P. Tsai, H.T. Yau, Relaxation of excited states in nonlinear Schrodinger equations, IMRN 2002 (2002) 31, 1629-1673.

TsaYau2002c T.P. Tsai, H.T. Yau, Stable directions for excited states of nonlinear Schrodinger equations, CPDE 27 (2002), 2363-2402.

TsaYau-p T.P. Tsai, H. T. Yau, Classification of asymptotic profiles of nonlinear Schrodinger equations with small initial data, preprint.

Tg2000 K. Tsugawa, Well-posedness in the energy space for the Cauchy problem of the coupled system of complex scalar field and Maxwell equations, Funkcial. Ekvac. 43 (2000), 127-161.

Tg-p K. Tsugawa, On the coupled system of non-linear wave equations with different propagation speeds in 1 and 2 spatial dimensions, preprint.

Ty1998 K. Tsutaya, Local regularity of non-resonant nonlinear wave equations, Diff. Integr. Eqns 11 (1998), 279-292.

Ts1984 Y. Tsutsumi, Nonrelativistic approximation of nonlinear Klein-Gordon equations in two space dimensions, Nonlinear Anal. 8 (1984), 637-643.

Ts1985 Y. Tsutsumi, Scattering problem for nonlinear Schrodinger equations, Ann. Inst. H. Poincare, Phys. Theor. 43 (1985), 321-347.

Ts1985b Y. Tsutsumi, Global existence and asymptotic behavior of solutions for nonlinear Schrodinger equations, Doctoral Thesis, U. Tokyo (1985)

Ts1987 Y. Tsutsumi, L^2 solutions for nonlinear Schrodinger equations and nonlinear groups, Funk. Ekva. 30 (1987), 115-125.

Ts1989 Y. Tsutsumi, The Cauchy problem for the Korteweg-de Vries equation with measures as initial data, SIAM J. Math. Anal. 20 (1989), 582-588.

Ts1990 Y. Tsutsumi, Rate of L^2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power. Nonlinear Anal. 15 (1990), no. 8, 719-724

Ts1993 Y. Tsutsumi, Global existence and asymptotic behaviour of solutions to the Maxwell-Schrodinger system in three space dimensions, CMP 151 (1993), 543-576.

Ts1994 Y. Tsutsumi, The null gauge condition and the one-dimensional nonlinear Schrödinger equation with cubic nonlinearity. Indiana Univ. Math. J. 43 (1994), no. 1, 241-254.

Ts1995 Y. Tsutsumi, Global existence and uniqueness of energy solutions for the Maxwell-Schrödinger equations in one space dimension. Hokkaido Math. J. 24 (1995), 617-639.

TsmFu1980 M. Tsutsumi, I. Fukuda, On solutions to the derivative nonlinear Schrodinger equation. Existence and Uniqueness theorem. Funk. Ekvac. 23 (1980), 259-277.

TsmFu1981 M. Tsutsumi, I. Fukuda, On solutions to the derivative nonlinear Schrodinger equation II. Funk. Ekvac. 24 (1981), 85-94.

TsNk1985 Y. Tsutsumi, K. Nakamitsu, Global existence of solutions to the Cauchy problem for coupled Maxwell-Schroedinger equations in two space dimensions, Lecture Notes in Pure and Appl. Math. 102, Dekker, New York 1985.

TsYa1984 Y. Tsutsumi, K. Yajima, The asymptotic behavior of nonlinear Schrodinger equations, Bull. AMS. 11 (1984) 186-188.

TrFl1985 S. Turitsyn, G. Falkovitch, Stability of magneto-elastic solitons and self-focusing of sound in antiferromagnet, Soviet Phys. JETP 62 (1985), 146-152.

Tzi-p N. Tzirakis, The Cauchy problem for the semilinear quintic Schrodinger equation in one dimension, the defocusing case, preprint.

Tz1999 N. Tzvetkov, On the Cauchy problem for Kadontsev-Petviashvili equations, Comm. PDE. 24 (1999), 1367-1397.

Tz1999b N. Tzvetkov, Remark on the local ill-posedness for KdV equation, C.R. Acad. Sci. Paris (1999), 1043-1047.

Tz-p N. Tzvetkov, Global low regularity solutions for Kadomtsev-Petviashvili equation, Diff. Int. Eq. (to appear).

Tz-p2 N. Tzvetkov, On the long-time behavior of KdV type equations (after Martel-Merle), preprint.

U

Uk1989 S. Ukai, Local solutions of the Kadomtsev-Petviashvili equation, J. Fac. Soc. Univ. Tokyo Sect. 1 A Math. 36 (1989), 193-209.

V

VaVe2001 A. Vargas, L. Vega, Global well-posedness for 1D nonlinear Schrodinger equation for data with an infinite L^2 norm, J. Math. Pures Appl. 80, (2001), 1029-1044.

Ve1988 L. Vega, Schrodinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), 874-878.

Ve1992 L. Vega, Restriction theorems and the Schrodinger multiplier on the torus, PDE with minimal smoothness and applications (Chicago 1990), IMA VolMath. Appl. 42 (1992), 199-211.

Vi2001 M. Vilela, Regularity of solutions to the free Schrodinger equation with radial initial data, Ill. J. Math. 45 (2001), 361-370.

Vd1984 M. V. Vladimirov, On the solvability of mixed problem for a nonlinear equation of Schrodinger type, Sov. Math. Dokl 29 (1984), 281-284.

W

Wal-p B. Walther, Higher integrability for maximal oscillatory Fourier integrals, preprint.

WghWgy2000 H. Wang, Y.D. Wang, Global inhomogeneous Schrodinger flow, Int. J. Math. 11 (2000), 1079

WgxAbSe1994 X. P. Wang, M. Ablowitz, H. Segur, Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation, Physica D 78 (1994), 241-265.

Wgy1995 Y.D. Wang, Ferromagnetic chain equation from a closed Riemannian manifold into S^2, Int. J. Math. 6 (1995), 93

Wed1999 R. Weder, The W_{k,p} continuity of the Schrodinger wave operators on the line, CMP 208 (1999), 507-520.

Wed1999b R. Weder, Inverse scattering for the nonlinear Schrodinger equation, CPDE 22 (1997), 2089-2103.

Wed2000 R. Weder, L^p - L^p' estimates for the Schrodinger equation on the line and inverse scattering for the nonlinear Schrodinger equation with a potential, JFA 170 (2000), 37-68.

Wed2000b R. Weder, Center manifold for nonintegrable nonlinear Schrodinger equations on the line, CMP 215 (2000), 343-356.

Wed2001 R. Weder, Inverse scattering for the nonlinear Schrodinger equation: reconstruction of the potential and the non-linearity, Math. Methods Appl. Sci. 24 (2001), 245-254.

Wed2001b R. Weder, Inverse scattering for the nonlinear Schrodinger equation II. reconstruction of the potential and the non-linearity in the multidimensional case, Proc. Amer. Math. Soc. 129 (2001), 3627-3645.

Wed2001c R. Weder, Direct and inverse scattering for the nonlinear Schrodinger equation with potential, VI Seminar on Free Boundary Value Problems and their Applications, part 1 (Rosario 1998), 13-20, Mat Ser. A. Conf. Semin. Trab. Math. 3, Univ. Austral, Rosario, 2001.

Wed2001d R. Weder, Inverse scattering on the line for the nonlinear Klein-Gordon equation with a potential. J. Math. Anal. Appl. 252 (2000), 102-123.

Wed2002 R. Weder, Multidimensional inverse scattering for the nonlinear Klein-Gordon equation with a potential, JDE 184 (2002), 62-77.

Wed-p R. Weder, The forced non-linear Schrodinger equation with a potential on the half-line, preprint.

Wed-p2 R. Weder, The L^p - L^p' estimate for the Schrodinger equation on the half-line, preprint.

Wed-p3 R. Weder, Scattering for the forced nonlinear Schrodinger equation with a potential on the half-line, preprint.

Ws1983 M. Weinstein, Nonlinear Schrodinger equations and sharp interpolation estimates, CMP 87 (1983), 567-576.

Ws1985 M. Weinstein, Modulational stability of ground states of nonlinear Schrodinger equations, SIAM J. Math. Anal. 16 (1985), 472-491.

Ws1986 M. Weinstein, Lyapunov stability of ground states of nonlinear dispersive equations, CPAM 39 (1986), 51-68.

Ws1986b M. Weinstein, On the structure and formation of singularities in solutions to nonlinear dispersive equations, CPDE 11 (1986), 545-565.

WsXi1996 M. Weinstein, J. Xin, Dynamic stability of vortex solutions of Ginzberg-Landau and nonlinear Schrodinger equations, CMP 180 (1996), 389-428.

Wc1987 M.V. Wickerhauser, Inverse scattering for the heat operators and evolutions in 2+1 variables, CMP 108 (1987) 67-89.

Wx1959 C. Wilcox, The initial boundary-value problem for the wave equation in an exterior domain with spherical boundary, Not. Amer. Math. Soc. 6 (1959).

Wo-p T. Wolff, A sharp bilinear cone estimate, to appear, Ann. Math.

Wol1984 S Wollman, An existence and uniqueness theorem for the Vlasov-Maxwell system, CPAM 37 (1984), 457-462.

Woo-p T. Woods, 1+1 Lorentz wave maps, preprint.

Wu1991 U. Wuller, Geometric methods in scattering theory of the charge transfer model, Duke Math J. 62 (1991), 273-313.

X
Y

Yag1994 K. Yagi, Normal forms and nonlinear Klein-Gordon equations in one space dimension, Master Thesis, Waseda University, 1994.

Ya1976 K. Yajima, Nonrelavistic limit of the Dirac theory, scattering theory, J. Fac. Sci. Univ. Tokyo. Sect. IA Math. 23 (1976), 517-523.

Ya1980 K. Yajima, A multichannel scattering theory for some time dependent Hamiltonians, charge transfer problem, CMP 75 (1980), 153-178.

Ya1987 K. Yajima, Existence of solutions for Schrodinger evolution equations, Commun. Math. Phys. 110 (1987), 415-426.

Ya1995 K. Yajima, The W^{k,p} continuity of wave operators for Schrodinger operators, J. Math. Soc. Japan 47 (1995), 551-581.

Ya1999 K. Yajima, The L^p continuity of wave operators for two-dimensional Schrodinger operators, CMP 208 (1999), 125-152.

YaZgg2001 K. Yajima, G. Zhang, Smoothing property for Schrodinger equations with potential superquadratic at infinity, CMP 221 (2001), 573-590.

Yk2000 K. Yokoyama, Global existence of classical solutions to systems of wave equations with critical nonlinearity in three space dimensions, J. Math. Soc. Japan 52 (2000), 609-632.

Yo-p B. Yordanov, Blow-up for the one-dimensional Klein-Gordon equation with a cubic non-linearity, preprint.

YoZgq-p B. Yordanov, Q. Zhang, Finite time blowup for wave equations with a potential, preprint.

YoZgq-p2 B. Yordanov, Q. Zhang, Finite time blowup for critical wave equations in high dimensions, preprint.

Z

ZaKru1965 N. Zabusky, M. Kruskal, Interaction of solitons in a collisionless plasma and the recurrence of initial states, Phys. Rev. Lett. 15 (1965), 240-243.

Zk1972 V.E. Zakharov, Collapse of Langmuir waves, Sov. Phys. JETP 35 (1972), 908-914.

Zk1998 V.E. Zakharov, Weakly nonlinear waves on the surface of an ideal finite depth fluid, Amer. Math. Soc. Transl. 182 (1998), 167-197.

ZkMan1976 V.E. Zakharov, S.V. Manakov, Asymptotic behavior of non-linear wave systems integrated by the inverse scattering method, Soviet Physics JETP 44 (1976), 106-112.

ZkSha1972 V.E. Zakharov, A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in non-linear media, Sov. Phys. JETP 34 (1972), 62-69.

ZkSha1973 V.E. Zakharov, A.B. Shabat, Interaction between solitons in a stable medium, Sov. Phys. JETP 37 (1973), 834-828.

ZkShl1980 V.E. Zakharov, E.I. Schulman, Degenerated dispersion laws, motion invariant and kinetic equations, Physica 1D (1980), 185-250.

ZkTkh1979 V.E. Zakharov, L.A. Takhtahan, Equivalence of a nonlinear Schrodinger equation and a Heisenberg ferromagnetic equation, Teor. Math. Phys. 8 (1979), 17-23.

Zg1992 B. Zhang, Unique continuation for the KdV equation, SIAM J. Math. Anal. 23 (1992), 55-71.

Zg1995 B. Zhang, A remark on the Cauchy problem for the Korteweg-de Vries equation on a periodic domain, DIE 8 (1995), 1191-1204.

Zg1997 B. Zhang, Unique continuation properties of the nonlinear Schrodinger equation, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), 191-205.

Zx1990 X. Zhou, Inverse scattering transform for the time-dependent Schrodinger equation with application to the KP-I equations, CMP 128 (1990), 551-564.

Zh1995 Y. Zhou, Cauchy problem for semilinear wave equations in four space dimensions with small initial data, JPDE 8 (1995), 135-144.

Zh1997 Y. Zhou, Local existence with minimal regularity for nonlinear wave equations, Amer. J. Math, 119 (1997), 671-703.

Zh1997b Y. Zhou, Uniqueness of weak solution of the KdV equation, IMRN 6 (1997), 271-283.

Zh1999 Y. Zhou, Uniqueness of weak solutions of 1+1 dimensional wave maps, Math. Z. 232 (1999), 707-719.

Zh2000 Y. Zhou, Uniqueness of generalized solutions to nonlinear wave equations, AJM 122 (2000), 939-965.

ZhGouTan1991 Y. Zhou, B. Gou, S. Tan, Existence and uniqueness of smooth solution for system of ferromagnetic chain, Science in China Ser. A. 34 (1991), 257.

Zi1997 L. Zielinski, Asymptotic completeness for multiparticle dispersive charge transfer models, JFA 150 (1997), 453-470.