Orbital stability of standing waves for a system of nonlinear Schr\"{o}dinger equations with three wave interaction
Analysis of PDEs
2017-12-05 v1
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 mass constraints. As a consequence, we establish existence and orbital stability of solitary waves.
Keywords
Cite
@article{arxiv.1709.09788,
title = {Orbital stability of standing waves for a system of nonlinear Schr\"{o}dinger equations with three wave interaction},
author = {Alex H. Ardila},
journal= {arXiv preprint arXiv:1709.09788},
year = {2017}
}
Comments
21 pages; revised version incorporating referees' comments