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

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