On traveling waves and global existence for a nonlinear Schrödinger system with three waves interaction

Abstract

In this paper, we consider three components system of nonlinear Schrödinger 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.

arXiv comment22 Page. arXiv admin note: text overlap with arXiv:2209.05305 by other authors