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| | == Dispersive PDE Wiki == |
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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]].) |
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| | 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! |
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| | 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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| | == Classes of equations == |
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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: |
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| | # [[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.) |
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| | # [[Schrodinger equations|Nonlinear Schrodinger equations]] ([[NLS equation|NLS]], [[Schrodinger maps|Schrodinger maps]], [[Cubic DNLS on R|DNLS]], [[Hartree equation|Hartree]], etc.) |
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| | # [[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.) |
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| | # [[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.) |
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| | A complete list of equations discussed on this wiki [[:Category:Equations|can be found here]]. |
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| | == Other Web resources == |
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| | *Wikipedia has a [http://en.wikipedia.org/wiki/Partial_differential_equations partial differential equations page]. |
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| | *There is a [http://en.wikipedia.org/wiki/Category:Mathematics-related_lists list of math related pages on wikipedia ]. |
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| | *Check out the [http://www.wikiwaves.org/index.php/Main_Page water waves wiki]. |
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