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arXiv · 1709.09788

Orbital stability of standing waves for a system of nonlinear Schr\"{o}dinger equations with three wave interaction

Alex H. Ardila
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Abstract

We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schr\"{o}dinger system related to the Raman amplification in a plasma. By means of the concentration-compacteness method, we provide a characterization of the standing waves solutions as minimizers of an energy functional subject to three independent $L^{2}$ mass constraints. As a consequence, we establish existence and orbital stability of solitary waves.

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Alex H. Ardila. 2017-09-28. Orbital stability of standing waves for a system of nonlinear Schr\"{o}dinger equations with three wave interaction. https://doi.org/10.1016/j.na.2017.10.013

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