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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]].)


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.


We welcome updates, corrections, and new contributions!  Please [[Help:Contents|click here]] for help on how to to do this.
== Classes of equations ==


== Classes of equations ==
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:
 
# [[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.)


There are many nonlinear dispersive and wave equations of interest, many of which arise from mathematical physics. We can divide them into four classes:
A complete list of equations discussed on this wiki [[:Category:Equations|can be found here]].


# [[Wave equations|Nonlinear wave equations]] ([[NLW equation|NLW]], [[NLKG equation|NLKG]], [[Wave maps equation|Wave maps]], [[Maxwell-Klein-Gordon equation|Maxwell-Klein-Gordon]], [[Yang-Mills equation|Yang-Mills]], [[Einstein equations|Einstein]], etc.)
== Other Web resources ==
# [[Schrodinger equations|Nonlinear Schrodinger equations]] ([[NLS equation|NLS]], [[Schrodinger map equation|Schrodinger maps]], etc.)
# [[KdV equations|Equations of Korteweg-de Vries type]] ([[Korteweg de Vries equation|KdV]], [[Modified Korteweg de Vries equation|mKdV]], [[Generalised Korteweg de Vries equation|gKdV]], etc.)
# [[Other equations]] ([[Kadomtsev-Petviashvili equation|Kadomtsev-Petviashvili]], [[Zakharov equation|Zakharov]], [[Davey-Stewartson system|Davey-Stewartson]], etc.)


A complete list of equations discussed on this page [[:Category:Equations|can be found here]].
*Wikipedia has a [http://en.wikipedia.org/wiki/Partial_differential_equations partial differential equations page].
*There is a [http://en.wikipedia.org/wiki/Category:Mathematics-related_lists list of math related pages on wikipedia] .
*Check out the [http://www.wikiwaves.org/index.php/Main_Page water waves wiki].

Latest revision as of 18:34, 10 June 2018

Welcome to the Dispersive PDE Wiki! These web pages are intended to present the latest results, conjectures, bibliography, concepts and other material on the local and global well-posedness problems (and related questions) for non-linear dispersive and wave equations. (We also have a more detailed description of this wiki and its purpose.)

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 create an account and you're ready to edit! If you are new to wikis, we have some help files available. If you are interested in contributing, you might want to visit our community portal for current discussions and projects.

Classes of equations

There are a large number of nonlinear dispersive and wave equations of interest, many of which arise from mathematical physics. We can divide them into four classes:

  1. Nonlinear wave equations (NLW, NLKG, Wave maps, Maxwell-Klein-Gordon, Yang-Mills, Einstein equations, etc.)
  2. Nonlinear Schrodinger equations (NLS, Schrodinger maps, DNLS, Hartree, etc.)
  3. Equations of Korteweg-de Vries type (KdV, mKdV, gKdV, etc.)
  4. Other equations and systems (Benjamin-Ono, Kadomtsev-Petviashvili, Zakharov, Davey-Stewartson, etc.)

A complete list of equations discussed on this wiki can be found here.

Other Web resources

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