Zakharov-Schulman system: Difference between revisions
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where L_1, L_2, L_3 are various constant coefficient differential operators; these describe the interactions of small amplitude, high frequency waves with acoustic waves [ZkShl1980]. Using energy methods and gauge transformations, local existence for smooth data was established in [KnPoVe1995b]; see also [GhSau1992]. | where L_1, L_2, L_3 are various constant coefficient differential operators; these describe the interactions of small amplitude, high frequency waves with acoustic waves [ZkShl1980]. Using energy methods and gauge transformations, local existence for smooth data was established in [KnPoVe1995b]; see also [GhSau1992]. | ||
The [[Davey-Stewartson system]] can be viewed as a special case of this system. | |||
[[Category:Equations]] | [[Category:Equations]] | ||
Revision as of 16:51, 30 July 2006
The Zakharov-Schulman system is described by the equations
i u_t + L_1 u = phi u
L_2 phi = L_3( |u|^2 )
where L_1, L_2, L_3 are various constant coefficient differential operators; these describe the interactions of small amplitude, high frequency waves with acoustic waves [ZkShl1980]. Using energy methods and gauge transformations, local existence for smooth data was established in [KnPoVe1995b]; see also [GhSau1992].
The Davey-Stewartson system can be viewed as a special case of this system.
