Zakharov-Schulman system: Difference between revisions
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The [[Zakharov-Schulman system]] is described by the equations | The [[Zakharov-Schulman system]] is described by the equations | ||
i u_t + L_1 u = phi u | <center><math>i u_t + L_1 u = \phi u</math></center> | ||
<center><math>L_2 \phi = L_3( |u|^2 )</math></center> | |||
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]. | 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. | The [[Davey-Stewartson system]] can be viewed as a special case of this system. | ||
[[Category:Equations]] | [[Category:Equations]] | ||
Latest revision as of 21:50, 5 August 2006
The Zakharov-Schulman system is described by the equations
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.
