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There are many nonlinear dispersive and wave equations of interest, many of which arise from mathematical physics. We can divide them into four classes: | There are many 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]] (NLW, NLKG, Wave maps, Maxwell-Klein-Gordon, Yang-Mills, Einstein, etc.) | # [[Wave equations|Nonlinear wave equations]] ([[NLW equation|NLW]], [[NLKG equation|NLKG]], [[Wave maps equation|Wave maps]], [[Maxwell-Klein-Gordon equation|Maxwell-Klein-Gordon]], [[Yang-Mills equation|Yang-Mills]], [[Einstein equations|Einstein]], etc.) | ||
# [[Schrodinger equations|Nonlinear Schrodinger equations]] (NLS, Schrodinger maps, etc.) | # [[Schrodinger equations|Nonlinear Schrodinger equations]] ([[NLS equation|NLS]], [[Schrodinger map equation|Schrodinger maps]], etc.) | ||
# [[KdV equations|Equations of Korteweg-de Vries type]] (KdV, mKdV, gKdV, etc.) | # [[KdV equations|Equations of Korteweg-de Vries type]] ([[Korteweg de Vries equation|KdV]], [[Modified Korteweg de Vries equation|mKdV]], [[Generalised Korteweg de Vries equation|gKdV]], etc.) | ||
# [[Other equations]] ([[Kadomtsev-Petviashvili equation|Kadomtsev-Petviashvili]], [[Zakharov equation|Zakharov]], Davey-Stewartson, etc.) | # [[Other equations]] ([[Kadomtsev-Petviashvili equation|Kadomtsev-Petviashvili]], [[Zakharov equation|Zakharov]], [[Davey-Stewartson system|Davey-Stewartson]], etc.) | ||
Revision as of 06:13, 27 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. (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:
- Nonlinear wave equations (NLW, NLKG, Wave maps, Maxwell-Klein-Gordon, Yang-Mills, Einstein, etc.)
- Nonlinear Schrodinger equations (NLS, Schrodinger maps, etc.)
- Equations of Korteweg-de Vries type (KdV, mKdV, gKdV, etc.)
- Other equations (Kadomtsev-Petviashvili, Zakharov, Davey-Stewartson, etc.)
