zbMATH — the first resource for mathematics

Stability of traveling-wave solutions for a Schrödinger system with power-type nonlinearities. (English) Zbl 1303.35102
Summary: 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.

MSC:
 35Q55 NLS equations (nonlinear Schrödinger equations) 35A15 Variational methods applied to PDEs 35B35 Stability in context of PDEs 35Q35 PDEs in connection with fluid mechanics 35C08 Soliton solutions
Full Text: