Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 217, pp. 1-16.
Title: Stability of traveling-wave solutions for a Schrodinger system
with power-type nonlinearities
Authors: Nghiem V. Nguyen (Utah State Univ., Logan, UT, USA)
Rushun Tian (Chinese Academy of Sciences, Beijing, China)
Zhi-Qiang Wang (Utah State Univ., Logan, UT, USA)
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