Electron. J. Diff. Equ., Vol. 2014 (2014), No. 217, pp. 1-16.

Stability of traveling-wave solutions for a Schrodinger system with power-type nonlinearities

Nghiem V. Nguyen, Rushun Tian, Zhi-Qiang Wang

Abstract:
In this article, we consider the Schrodinger system with power-type nonlinearities,
$$ i\frac{\partial}{\partial t}u_j+ \Delta u_j + a|u_j|^{2p-2} u_j + \sum_{k=1, k\neq j}^m b |u_k|^{p}|u_j|^{p-2} u_j=0; \quad x\in \mathbb{R}^N, $$
where $j=1,\dots,m$, $u_j$ are complex-valued functions of $(x,t)\in \mathbb{R}^{N+1}$, a,b are real numbers. It is shown that when $b>0$, and $a+(m-1)b>0$, for a certain range of p, traveling-wave solutions of this system exist, and are orbitally stable.

Submitted November 22, 2013. Published October 16, 2014.
Math Subject Classifications: 35A15, 35B35, 35Q35, 35Q55.
Key Words: solitary wave solutions; stability; nonlinear Schrodinger system; traveling-wave solutions

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Nghiem V. Nguyen
Department of Mathematics and Statistics
Utah State University, Logan, UT 84322, USA
email: nghiem.nguyen@usu.edu
Rushun Tian
Academy of Mathematics and System Science
Chinese Academy of Sciences
Beijing 100190, China
email: rushun.tian@amss.ac.cn
  Zhi-Qiang Wang
Department of Mathematics and Statistics
Utah State University, Logan, UT 84322, USA
email: zhiqiang.wang@usu.edu

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