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Existence and uniqueness of solutions for a type of generalized Zakharov system. (English) Zbl 1397.35283

Summary: We study the Cauchy problem for a type of generalized Zakharov system. With the help of energy conservation and approximate argument, we obtain global existence and uniqueness in Sobolev spaces for this system. Particularly, this result implies the existence of classical solution for this generalized Zakharov system.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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