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on the local and global [[well-posedness]] problem (and related questions) for non-linear dispersive and wave equations. (We also have [[DispersiveWiki:About|a more detailed description of this wiki and its purpose]].) | on the local and global [[well-posedness]] problem (and related questions) for non-linear 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! | 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 | 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. | ||
== Classes of equations == | == Classes of equations == | ||
Revision as of 04:20, 5 August 2006
Dispersive PDE Wiki
Welcome to the Dispersive PDE Wiki! These web pages are intended to present the latest results, conjectures, bibliography and other material on the local and global well-posedness problem (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:
- Nonlinear wave equations (NLW, NLKG, Wave maps, Maxwell-Klein-Gordon, Yang-Mills, Einstein, etc.)
- Nonlinear Schrodinger equations (NLS, Schrodinger maps, DNLS, Hartree, etc.)
- Equations of Korteweg-de Vries type (KdV, mKdV, gKdV, etc.)
- 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 topics
We have a list of concepts used in the analysis of dispersive PDE.
