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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
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