English

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 L2L^{2} 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