# Difference between revisions of "Davey-Stewartson system"

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The Davey-Stewartson system is a special case of the [[Zakharov-Schulman system]]. | The Davey-Stewartson system is a special case of the [[Zakharov-Schulman system]]. | ||

+ | [[Category:Integrability]] | ||

[[Category:Equations]] | [[Category:Equations]] |

## Revision as of 07:35, 31 July 2006

The **Davey-Stewartson system** [DavSte1974] in 2 spatial dimensions involves a complex field u and a real field phi:

The field phi depends elliptically on u when is positive and thus one usually only specifies the initial data for , not . This equation is a two-dimensional modification of the one-dimensional cubic nonlinear Schrodinger equation and is completely integrable in the cases (DS-I) and (DS-II). When the situation becomes a nonlinear Schrodinger equation with non-local nonlinearity, and can be treated by Strichartz estimates [GhSau1990]; for the situation is quite different but one can still use derivative NLS techniques (i.e. gauge transforms and energy methods) to obtain some local existence results [LiPo1993]. Further results are in [HaSau1995].

The Davey-Stewartson system is a special case of the Zakharov-Schulman system.