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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: | 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: | ||
# [[Wave equations|Nonlinear wave equations]] ([[semilinear NLW|NLW]], [[semilinear NLW|NLKG]], [[ | # [[Wave equations|Nonlinear wave equations]] ([[semilinear NLW|NLW]], [[semilinear NLW|NLKG]], [[wave maps|Wave maps]], [[Maxwell-Klein-Gordon equation|Maxwell-Klein-Gordon]], [[Yang-Mills equation|Yang-Mills]], [[Einstein Equations|Einstein]], etc.) | ||
# [[Schrodinger equations|Nonlinear Schrodinger equations]] ([[NLS equation|NLS]], [[Schrodinger maps|Schrodinger maps]], [[Cubic DNLS on R|DNLS]], [[Hartree equation|Hartree]], 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.) | # [[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.) | ||
Revision as of 06:39, 29 July 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! If you are new to editing 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.
