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

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.