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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:

1. Nonlinear wave equations (NLW, NLKG, Wave maps, Maxwell-Klein-Gordon, Yang-Mills, Einstein, 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 topics

We have a list of concepts used in the analysis of dispersive PDE.