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Dispersive PDE Wiki

Local and global well-posedness for non-linear dispersive and wave equations

Maintained by Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka, and Terry Tao

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Purpose of this page

Bibliography

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The big three: Wave, Schrodinger, KdV

Wave equations	Schrodinger equations	KdV equations
Wave estimates wave:Linear estimates wave:Bilinear estimates wave:Multilinear estimates	Schrodinger estimates schrodinger:Linear estimates schrodinger:Bilinear estimates schrodinger:Trilinear estimates schrodinger:Multilinear estimates	kdv:Linear estimates kdv:Bilinear estimates kdv:Trilinear estimates kdv:Multilinear estimates
[wave:semilinear Semilinear NLW/NLKG]] wave:Scattering for NLW references:Scattering for NLKG wave:Sine-Gordon		kdv:gKdV on R^+
[[wave:nlw-2 Quadratic NLW/NLKG]	[[schrodinger:Quadratic_NLS_on_R NLS-2 on R] schrodinger:Quartic_NLS_on_R^2 NLS-2 on R^2 schrodinger:Quadratic_NLS_on_R^3 NLS-2 on R^3 schrodinger:Quadratic_NLS_on_T NLS-2 on T schrodinger:Quadratic_NLS_on_T^2 NLS-2 on T^2	kdv:kdv KdV (gKdV-1) kdv:kdv on R KdV on R kdv:kdv on T KdV on T kdv:kdv on R+ KdV on R^+
Cubic NLW/NLKG wave:nlw-3 on R NLW-3 on R wave:nlw-3 on R^2 NLW-3 on R^2 wave:nlw-3 on R^3 NLW-3 on R^3	Cubic NLS schrodinger:Cubic_NLS_on_R NLS-3 on R schrodinger:Cubic_NLS_on_R^2 NLS-3 on R^2 schrodinger:Cubic_NLS_on_R^3 NLS-3 on R^3 schrodinger:Cubic_NLS_on_R^4 NLS-3 on R^4 schrodinger:Cubic_NLS_on_T NLS-3 on T schrodinger:Cubic_NLS_on_T^2 NLS-3 on T^2 schrodinger:Cubic_NLS_on_T^4 NLS-3 on T^4 schrodinger:Cubic_NLS_on_RxT NLS-3 on R x T schrodinger:Cubic_NLS_on_S^6 NLS-3 on S^6	kdv:mkdv Modified KdV (gKdV-2) kdv:mKdV on R mKdV on R kdv:mKdV on T mKdV on T
	Quartic NLS schrodinger:Quartic_NLS_on_R NLS-4 on R schrodinger:Quartic_NLS_on_T NLS-4 on T schrodinger:Quartic_NLS_on_R^2 NLS-4 on R^2	gKdV-3 kdv:gKdV_3 on R gKdV-3 on R kdv:gKdV_3 on T gKdV-3 on T
Quintic NLW/NLKG wave:nlw-5 on R NLW-5 on R wave:nlw-5 on R^2 NLW-5 on R^2 wave:nlw-5 on R^3 NLW-5 on R^3	Quintic NLS schrodinger:Quintic_NLS_on_R NLS-5 on R schrodinger:Quintic_NLS_on_R^2 NLS-5 on R^2 schrodinger:Quintic_NLS_on_R^3 NLS-5 on R^3 schrodinger:Quintic_NLS_on_T NLS-5 on T	gKdV-4 kdv:gKdV_4 on R gKdV-4 on R kdv:gKdV_4 on T gKdV-4 on T
Septic NLW/NLKG wave.htm#nlw-7 on R NLW-7 on R wave.htm#nlw-7 on R^2 NLW-7 on R^2 wave.htm#nlw-7 on R^3 NLW-7 on R^3	Septic NLS schrodinger:Septic_NLS_on_R NLS-7 on R schrodinger:Septic_NLS_on_R^2 NLS-7 on R^2 schrodinger:Septic_NLS_on_R^3 NLS-7 on R^3
wave:gwp d-nlw GWP for D-NLW wave:gwp d-nlkg GWP for D-NLKG
wave:mkg MKG wave:mkg on R MKG on R wave:mkg on R^2 MKG on R^2 wave:mkg on R^3 MKG on R^3 wave:mkg on R^4 MKG on R^4 wave:mkg on R^5+ MKG on R^5+ wave:YM Yang Mills references:YM on R^2 YM on R^2 wave:YM on R^3 YM on R^3 wave:YM on R^4 YM on R^4 wave:ym on R^5+ YM on R^5+ wave:YMH on R^3 YMH on R^3 wave:Maxwell-Dirac Maxwell-Dirac wave:Dirac-Klein-Gordon Dirac-Klein-Gordon wave:two-speed DNLW Two-speed DNLW-2	Quadratic DNLS schrodinger:Maxwell-Schrodinger Maxwell-Schrodinger
	Cubic DNLS schrodinger:dnls-3 on R DNLS-3 on R
wave:wm Wave maps wave:wm on R WM on R wave:wm on R^2 WM on R^2 wave:two-speed DDNLW Two-speed DDNLW	DDNLS schrodinger:smaps Schrodinger Maps
wave:gwp qnlw GWP for QNLW wave:Einstein Einstein equations	Quasilinear NLS

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misc.html Other equations:

• Schrodinger-Ginsberg-Landau
• misc:Vlasov-Maxwell Vlasov-Maxwell
• misc:KP The Kadomtsev-Petvisasvhili equations
  • misc:KP-I Kadomtsev-Petviashvili I
  • misc:KP-II Kadomtsev-Petviashvili II
• misc:Zakharov Zakharov
  • misc:Zakharov-1 Zakharov on R and T
  • misc:Zakharov-2 Zakharov on R^2
  • misc:Zakharov-3 Zakharov on R^3
  • Klein-Gordon-Zakharov
  • misc:WS Other Wave-Schrodinger systems
    • Ishimori
    • Davey-Stewartson
    • Yukawa