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

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

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

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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.

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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.

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

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

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

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

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

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

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

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

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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.

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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.

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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.

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

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

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V. Banica, Remarks on the blowup for the nonlinear Schrodinger equation with critical mass on a plane domain, preprint.

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

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

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

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

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

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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.

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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.

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

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

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

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

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

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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.

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

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

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

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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.

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

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

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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.

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

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

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

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

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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.

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

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

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

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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.

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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.

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

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

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

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

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

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

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

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

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

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

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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.

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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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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.

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

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

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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.

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

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

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

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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.

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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.

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N. Burq, Global Strichartz estimates for nontrapping geometries: A remark about an article by H. Smith and C. Sogge, preprint.

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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.

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

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

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

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

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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.

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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.

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

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

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

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

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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.

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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.

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

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

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

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

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

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

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

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

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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).

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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.

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

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

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

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

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

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

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

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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.

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

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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.

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

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

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

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

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

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