On traveling waves and global existence for a nonlinear Schr\"odinger system with three waves interaction

Abstract

In this paper, we consider three components system of nonlinear Schr\"odinger equations related to the Raman amplification in a plasma. By using variational method, a new result on the existence of traveling wave solutions are obtained under the non-mass resonance condition. We also study the new global existence result for oscillating data. Both of our results essentially due to the absence of Galilean symmetry in the system.