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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. (Click here for a more detailed description of this wiki and its purpose.)

We welcome updates, corrections, and new contributions! Please click here for help on how to to do this.

Classes of equations

There are many 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, etc.)
3. Equations of Korteweg-de Vries type (KdV, mKdV, gKdV, etc.)
4. Other equations (Kadomtsev-Petviashvili, Zakharov, Davey-Stewartson, etc.)

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