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Welcome to the '''Dispersive PDE Wiki'''! These web pages are intended to present the latest results, [[:Category:Open problems|conjectures]], [[:Category:Bibliography|bibliography]], [[:Category:Concept|concepts]] and other material on the local and global [[well-posedness]] problems (and related questions) for non-linear [[dispersion relation|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 — just [[Special:Userlogin&type=signup|create an account]] and you're ready to edit! | |||
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 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. | 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. | ||
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There are a [[:Category:Equations|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 [[:Category:Equations|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]], [[Maxwell-Klein-Gordon equations|Maxwell-Klein-Gordon]], [[Yang-Mills equations|Yang-Mills]], [[Einstein equations]], 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.) | ||
# [[Other equations|Other equations and systems]] ([[Benjamin-Ono equation|Benjamin-Ono]], [[Kadomtsev-Petviashvili equation|Kadomtsev-Petviashvili]], [[Zakharov equation|Zakharov]], [[Davey-Stewartson system|Davey-Stewartson]], etc.) | # [[Other equations|Other equations and systems]] ([[Benjamin-Ono equation|Benjamin-Ono]], [[Kadomtsev-Petviashvili equation|Kadomtsev-Petviashvili]], [[Zakharov equation|Zakharov]], [[Davey-Stewartson system|Davey-Stewartson]], etc.) | ||
A complete list of equations discussed on this wiki [[:Category:Equations|can be found here]] | A complete list of equations discussed on this wiki [[:Category:Equations|can be found here]]. | ||
== Other Web | == Other Web resources == | ||
*Wikipedia has a [http://en.wikipedia.org/wiki/Partial_differential_equations partial differential equations page] . | *Wikipedia has a [http://en.wikipedia.org/wiki/Partial_differential_equations partial differential equations page]. | ||
*There is a [http://en.wikipedia.org/wiki/Category:Mathematics-related_lists list of math related pages on wikipedia ]. | *There is a [http://en.wikipedia.org/wiki/Category:Mathematics-related_lists list of math related pages on wikipedia] . | ||
*Check out the [http://www.wikiwaves.org/index.php/Main_Page water waves wiki]. | *Check out the [http://www.wikiwaves.org/index.php/Main_Page water waves wiki]. | ||
Latest revision as of 18:34, 10 June 2018
Welcome to the Dispersive PDE Wiki! These web pages are intended to present the latest results, conjectures, bibliography, concepts and other material on the local and global well-posedness problems (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 equations, 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 Web resources
- Wikipedia has a partial differential equations page.
- There is a list of math related pages on wikipedia .
- Check out the water waves wiki.
