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Analytic smoothing effect for a system of Schrödinger equations with two wave interaction. (English) Zbl 1319.35238

Summary: We study the global Cauchy problem for a system of Schrödinger equations with two wave interaction of quadratic, cubic and quintic degrees. For sufficiently small data with exponential decay at infinity we prove the existence and uniqueness of global solutions which are analytic with respect to Galilei and/or pseudo-conformal generators for sufficiently small data with exponential decay at infinity. This paper is a sequel to our paper [“Analytic smoothing effect for a system of Schrödinger equations with three wave interaction”, to appear], where three wave interaction is studied. We also discuss the associated Lagrange structure.

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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Full Text: Euclid