Advances in Differential Equations

Analytic smoothing effect for a system of Schrödinger equations with two wave interaction

Gaku Hoshino and Tohru Ozawa

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Abstract

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 [22], where three wave interaction is studied. We also discuss the associated Lagrange structure.

Article information

Source
Adv. Differential Equations Volume 20, Number 7/8 (2015), 697-716.

Dates
First available in Project Euclid: 8 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.ade/1431115713

Mathematical Reviews number (MathSciNet)
MR3344615

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Hoshino, Gaku; Ozawa, Tohru. Analytic smoothing effect for a system of Schrödinger equations with two wave interaction. Adv. Differential Equations 20 (2015), no. 7/8, 697--716. https://projecteuclid.org/euclid.ade/1431115713.


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