On asymptotic stability of nonlinear waves
On asymptotic stability of nonlinear waves
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DOI：
10.5802/slsedp.111
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
M. Kowalczyk;Y. Martel;Claudio Muñoz
中科院分区：
文献类型：
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作者：
M. Kowalczyk;Y. Martel;Claudio Muñoz
本文综述了几种色散或波动模型，如非线性薛定谔方程、推广的Korteweg-de Vries方程、非线性波动和Klein-Gordon方程的渐近稳定性的一些结果。然后，我们集中讨论了作者关于奇摄动下φ方程扭结的渐近稳定性的最新结果。我们还给出了一些非线性Klein-Gordon方程不存在小呼吸子的两个结果(其中一个以前似乎未知)。
We review some results on asymptotic stability of nonlinear waves for a few dispersive or wave models, like the nonlinear Schrödinger equation, the generalized Korteweg-de Vries equation, and the nonlinear wave and Klein-Gordon equations. Then, we focus on recent results of the authors concerning the asymptotic stability of the kink for the φ equation under odd perturbations. We also present two results (one of which seems previously unknown) of non-existence of small breathers for some nonlinear Klein-Gordon equations.