We study the global Cauchy problem for a system of Schrödinger equations with two wave interaction of quadratic, cubic and quintic degrees. For suciently small data with exponential decay at innity we prove the existence and uniqueness of global solutions which are analytic with respect to Galilei and/or pseudo-conformal generators for suciently small data with exponential decay at innity. This paper is a sequel to our paper , where three wave interaction is studied. We also discuss the associated Lagrange structure.
|Number of pages||20|
|Journal||Advances in Differential Equations|
|Publication status||Published - 2015 Jul 1|
ASJC Scopus subject areas
- Applied Mathematics