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== Dispersive PDE Wiki ==
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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, [[: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]].)
 
  
 
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!   
 
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!   
 
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.
 
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.
 
Due to a recent explosion of spam, edits to the Dispersive PDE Wiki will require an email confirmation. [[User:Colliand|Colliand]] 02:11, 12 June 2007 (EDT)
 
 
'''The machine hosting the dispersive wiki has been having problems. The U. Toronto Mathematics computing staff is investigating the situation and we hope to have it soon resolved.''' [[User:Colliand|Colliand]] 10:36, 27 August 2007 (EDT)
 
  
 
== Classes of equations ==
 
== Classes of equations ==

Revision as of 22:07, 3 September 2007

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