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arXiv · 2308.03408

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

Yuan Li
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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.

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Yuan Li. 2023-08-07. On traveling waves and global existence for a nonlinear Schr\"odinger system with three waves interaction. https://arxiv.org/abs/2308.03408

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