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| == Dispersive PDE Wiki ==
| | Welcome to the '''Dispersive PDE Wiki'''! These web pages are intended to present the latest results, [[:Category:Open problems|conjectures]], [[:Category:Bibliography|bibliography]], [[:Category:Concept|concepts]] and other material on the local and global [[well-posedness]] problems (and related questions) for non-linear [[dispersion relation|dispersive]] and [[wave equations]]. (We also have [[DispersiveWiki:About|a more detailed description of this wiki and its purpose]].) |
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| Welcome to the Dispersive PDE Wiki! These web pages are intended to present the latest results, conjectures, [[bibliography]] and other material
| | The information here has only recently been converted into wiki format, and there are still several rough edges to it. We welcome updates, corrections, cleanup, and new contributions — just [[Special:Userlogin&type=signup|create an account]] and you're ready to edit! |
| on the local and global [[well-posedness]] problem (and related questions) for non-linear dispersive and wave equations. ([[DispersiveWiki:About|Click here]] for a more detailed description of this wiki and its purpose.)
| | If you are new to wikis, we have some [[Help:Contents|help files]] available. If you are interested in contributing, you might want to visit our [[DispersiveWiki:Community Portal|community portal]] for current discussions and projects. |
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| We welcome updates, corrections, and new contributions! Please [[Help:Contents|click here]] for help on how to to do this.
| | == Classes of equations == |
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| <div class="MsoNormal" style="text-align: center"><center>
| | There are a [[:Category:Equations|large number]] of [[nonlinear]] [[dispersive]] and [[wave]] equations of interest, many of which arise from mathematical physics. We can divide them into four classes: |
| ----
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| </center></div>
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| <center>The big three: Wave, Schrodinger, KdV</center>
| | # [[Wave equations|Nonlinear wave equations]] ([[semilinear NLW|NLW]], [[semilinear NLW|NLKG]], [[Wave maps]], [[Maxwell-Klein-Gordon equations|Maxwell-Klein-Gordon]], [[Yang-Mills equations|Yang-Mills]], [[Einstein equations]], etc.) |
| | # [[Schrodinger equations|Nonlinear Schrodinger equations]] ([[NLS equation|NLS]], [[Schrodinger maps|Schrodinger maps]], [[Cubic DNLS on R|DNLS]], [[Hartree equation|Hartree]], etc.) |
| | # [[KdV equations|Equations of Korteweg-de Vries type]] ([[Korteweg-de Vries equation|KdV]], [[Modified Korteweg-de Vries equation|mKdV]], [[Generalized Korteweg-de Vries equation|gKdV]], etc.) |
| | # [[Other equations|Other equations and systems]] ([[Benjamin-Ono equation|Benjamin-Ono]], [[Kadomtsev-Petviashvili equation|Kadomtsev-Petviashvili]], [[Zakharov equation|Zakharov]], [[Davey-Stewartson system|Davey-Stewartson]], etc.) |
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| {| style="width: 100.0%; mso-cellspacing: 1.5pt; mso-padding-alt: 0in 0in 0in 0in" width="100%" border="1"
| | A complete list of equations discussed on this wiki [[:Category:Equations|can be found here]]. |
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| [[Wave equations]] | |
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| [[Schrodinger equations]]
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| [[KdV equations]]
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| [[Wave estimates]]
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| * [[wave:Linear estimates]]
| | == Other Web resources == |
| * [[wave:Bilinear estimates]]
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| * [[wave:Multilinear estimates]]
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| | style="padding: .75pt .75pt .75pt .75pt" |
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| [[Schrodinger estimates]]
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| * [[schrodinger:Linear estimates]] | | *Wikipedia has a [http://en.wikipedia.org/wiki/Partial_differential_equations partial differential equations page]. |
| * [[schrodinger:Bilinear estimates]]
| | *There is a [http://en.wikipedia.org/wiki/Category:Mathematics-related_lists list of math related pages on wikipedia] . |
| * [[schrodinger:Trilinear estimates]]
| | *Check out the [http://www.wikiwaves.org/index.php/Main_Page water waves wiki]. |
| * [[schrodinger:Multilinear estimates]]
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| [[kdv:Airy estimates]]
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| * [[kdv:Linear estimates]]
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| * [[kdv:Bilinear estimates]]
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| * [[kdv:Trilinear estimates]]
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| * [[kdv:Multilinear estimates]]
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| |-
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| | style="padding: .75pt .75pt .75pt .75pt" |
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| [wave:semilinear Semilinear NLW/NLKG]]
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| * [[wave:Scattering for NLW]]
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| * [[references:Scattering for NLKG]]
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| * [[wave:Sine-Gordon]]
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| [[schrodinger:Semilinear NLS]]
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| [[kdv:gKdV]]
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| * [[kdv:gKdV on R^+]] | |
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| [[wave:nlw-2 Quadratic NLW/NLKG]
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| [[schrodinger:Quadratic NLS]]
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| * [[schrodinger:Quadratic_NLS_on_R NLS-2 on R]
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| * [[schrodinger:Quartic_NLS_on_R^2 NLS-2 on R^2]]
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| * [[schrodinger:Quadratic_NLS_on_R^3 NLS-2 on R^3]]
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| * [[schrodinger:Quadratic_NLS_on_T NLS-2 on T]]
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| * [[schrodinger:Quadratic_NLS_on_T^2 NLS-2 on T^2]]
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| [[kdv:kdv KdV]] (gKdV-1)
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| * [[kdv:kdv on R KdV on R]]
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| * [[kdv:kdv on T KdV on T]]
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| * [[kdv:kdv on R+ KdV on R^+]]
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| |-
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| Cubic NLW/NLKG
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| * [[wave:nlw-3 on R NLW-3 on R]]
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| * [[wave:nlw-3 on R^2 NLW-3 on R^2]]
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| * [[wave:nlw-3 on R^3 NLW-3 on R^3]]
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| | style="padding: .75pt .75pt .75pt .75pt" |
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| Cubic NLS
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| * [[schrodinger:Cubic_NLS_on_R NLS-3 on R]]
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| * [[schrodinger:Cubic_NLS_on_R^2 NLS-3 on R^2]]
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| * [[schrodinger:Cubic_NLS_on_R^3 NLS-3 on R^3]]
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| * [[schrodinger:Cubic_NLS_on_R^4 NLS-3 on R^4]]
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| * [[schrodinger:Cubic_NLS_on_T NLS-3 on T]]
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| * [[schrodinger:Cubic_NLS_on_T^2 NLS-3 on T^2]]
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| * [[schrodinger:Cubic_NLS_on_T^4 NLS-3 on T^4]]
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| * [[schrodinger:Cubic_NLS_on_RxT NLS-3 on R x T]]
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| * [[schrodinger:Cubic_NLS_on_S^6 NLS-3 on S^6]]
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| | style="padding: .75pt .75pt .75pt .75pt" |
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| [[kdv:mkdv Modified KdV]] (gKdV-2)
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| * [[kdv:mKdV on R mKdV on R]]
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| * [[kdv:mKdV on T mKdV on T]]
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| |-
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| [[wave:nlw-4 Quartic NLW/NLKG]]
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| Quartic NLS
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| * [[schrodinger:Quartic_NLS_on_R NLS-4 on R]]
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| * [[schrodinger:Quartic_NLS_on_T NLS-4 on T]]
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| * [[schrodinger:Quartic_NLS_on_R^2 NLS-4 on R^2]]
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| | style="padding: .75pt .75pt .75pt .75pt" |
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| gKdV-3
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| * [[kdv:gKdV_3 on R gKdV-3 on R]] | |
| * [[kdv:gKdV_3 on T gKdV-3 on T]]
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| |-
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| Quintic NLW/NLKG
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| * [[wave:nlw-5 on R NLW-5 on R]]
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| * [[wave:nlw-5 on R^2 NLW-5 on R^2]]
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| * [[wave:nlw-5 on R^3 NLW-5 on R^3]]
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| Quintic NLS
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| * [[schrodinger:Quintic_NLS_on_R NLS-5 on R]]
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| * [[schrodinger:Quintic_NLS_on_R^2 NLS-5 on R^2]]
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| * [[schrodinger:Quintic_NLS_on_R^3 NLS-5 on R^3]]
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| * [[schrodinger:Quintic_NLS_on_T NLS-5 on T]]
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| | style="padding: .75pt .75pt .75pt .75pt" |
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| gKdV-4
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| * [[kdv:gKdV_4 on R gKdV-4 on R]]
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| * [[kdv:gKdV_4 on T gKdV-4 on T]]
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| |-
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| Septic NLW/NLKG
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| * [[wave.htm#nlw-7 on R NLW-7 on R]]
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| * [[wave.htm#nlw-7 on R^2 NLW-7 on R^2]]
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| * [[wave.htm#nlw-7 on R^3 NLW-7 on R^3]]
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| | style="padding: .75pt .75pt .75pt .75pt" |
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| Septic NLS
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| * [[schrodinger:Septic_NLS_on_R NLS-7 on R]]
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| * [[schrodinger:Septic_NLS_on_R^2 NLS-7 on R^2]]
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| * [[schrodinger:Septic_NLS_on_R^3 NLS-7 on R^3]]
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| |-
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| [[wave:dnlw D-NLW]]
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| * [[wave:gwp d-nlw GWP for D-NLW]]
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| * [[wave:gwp d-nlkg GWP for D-NLKG]]
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| [[schrodinger:d-nls D-NLS]]
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| [[kdv:hierarchy The KdV hierachy]]
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| [[wave:dnlw-2 Quadratic DNLW]]
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| * [[wave:mkg MKG]]
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| ** [[wave:mkg on R MKG on R]]
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| ** [[wave:mkg on R^2 MKG on R^2]]
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| ** [[wave:mkg on R^3 MKG on R^3]]
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| ** [[wave:mkg on R^4 MKG on R^4]]
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| ** [[wave:mkg on R^5+ MKG on R^5+]]
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| * [[wave:YM Yang Mills]]
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| ** [[references:YM on R^2 YM on R^2]]
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| ** [[wave:YM on R^3 YM on R^3]]
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| ** [[wave:YM on R^4 YM on R^4]]
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| ** [[wave:ym on R^5+ YM on R^5+]]
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| ** [[wave:YMH on R^3 YMH on R^3]]
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| * [[wave:Maxwell-Dirac Maxwell-Dirac]]
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| * [[wave:Dirac-Klein-Gordon Dirac-Klein-Gordon]]
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| * [[wave:two-speed DNLW Two-speed DNLW-2]]
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| | style="padding: .75pt .75pt .75pt .75pt" |
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| Quadratic DNLS
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| * [[schrodinger:Maxwell-Schrodinger Maxwell-Schrodinger]]
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| Cubic DNLS
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| * [[schrodinger:dnls-3 on R DNLS-3 on R]]
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| [[wave:ddnlw DDNLW]]
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| * [[wave:wm Wave maps]]
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| ** [[wave:wm on R WM on R]]
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| ** [[wave:wm on R^2 WM on R^2]]
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| * [[wave:two-speed DDNLW Two-speed DDNLW]]
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| | style="padding: .75pt .75pt .75pt .75pt" |
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| DDNLS
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| * [[schrodinger:smaps Schrodinger Maps]]
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| [[wave:Quasilinear Quasilinear NLW]]
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| * [[wave:gwp qnlw GWP for QNLW]]
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| * [[wave:Einstein Einstein equations]]
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| Quasilinear NLS
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| [[schrodinger:Hartree Hartree equation]]
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| [[kdv:Benjamin-Ono Benjamin-Ono equation]]
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| |}
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| <div class="MsoNormal" style="text-align: center"><center>
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| ----
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| </center></div>
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| <center>[[misc.html Other equations]]<nowiki>:</nowiki></center>
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| * Schrodinger-Ginsberg-Landau
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| * [[misc:Vlasov-Maxwell Vlasov-Maxwell]]
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| * [[misc:KP The Kadomtsev-Petvisasvhili equations]]
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| ** [[misc:KP-I Kadomtsev-Petviashvili I]]
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| ** [[misc:KP-II Kadomtsev-Petviashvili II]]
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| * [[misc:Zakharov Zakharov]]
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| ** [[misc:Zakharov-1 Zakharov on R and T]]
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| ** [[misc:Zakharov-2 Zakharov on R^2]]
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| ** [[misc:Zakharov-3 Zakharov on R^3]]
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| ** Klein-Gordon-Zakharov
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| ** [[misc:WS Other Wave-Schrodinger systems]]
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| *** Ishimori
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| *** Davey-Stewartson
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| *** Yukawa
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| </div>
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