Orbital stability of periodic waves for the nonlinear Schrödinger equation

被引：0
作者：
Thierry Gallay
Mariana Hǎrǎgus
机构：
[1] Université de Grenoble I,Institut Fourier
[2] Université de Franche-Comté,Département de Mathématiques
来源：
Journal of Dynamics and Differential Equations | 2007年 / 19卷
关键词：
Nonlinear Schrödinger equation; periodic waves; orbital stability;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The nonlinear Schrödinger equation has several families of quasi-periodic traveling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the same period and the same Floquet exponent. This generalizes a previous work (Gallay and Haragus, J. Diff. Equations, 2007) where only small amplitude solutions were considered. A similar result is obtained in the focusing case, under a non-degeneracy condition which can be checked numerically. The proof relies on the general approach to orbital stability as developed by Grillakis, Shatah, and Strauss, and requires a detailed analysis of the Hamiltonian system satisfied by the wave profile.
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页码：825 / 865
页数：40
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