On traveling waves for a nonlinear Schrödinger system with three waves interaction

In this paper, we investigate a three-component system of nonlinear Schrödinger equations associated with Raman amplification in a plasma. By using a variational method, we obtain a novel result on the existence of traveling wave solutions under the non-mass resonance condition. Subsequently, we analyze the high frequency limit of the traveling waves as ω → ∞ and the traveling wave velocity is bounded. Finally, we give a new global existence result for oscillating data. Both of our results are essentially due to the absence of Galilean symmetry in the system.