Periodic waves of the Lugiato–Lefever equation at the onset of Turing instability
Periodic waves of the Lugiato–Lefever equation at the onset of Turing instability
复制标题
图灵不稳定性开始时 Lugiato-Lefever 方程的周期波
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Mariana Haraguss
中科院分区：
文献类型：
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作者：
Lucie Delcey;Mariana Haraguss
本文研究了一类非线性光学模型Lugiato-Lefever方程周期稳定波的存在性和稳定性。从一个详细的描述的稳定性常数的解决方案，然后我们专注于周期稳定波的图灵不稳定性的发病分叉。利用中心流形约化，我们分析了这些图灵分支，并证明了周期稳定波的存在性。这种方法也使我们能够得出结论，这些波的非线性轨道稳定性的共周期扰动，即周期扰动具有相同的周期的波。这个稳定性结果是由一般有界扰动的谱稳定性结果完成的。特别是，这种频谱分析表明，不稳定性总是由于共周期扰动。本文是“非线性波和模式的稳定性及相关主题”主题的一部分。
We study the existence and the stability of periodic steady waves for a nonlinear model, the Lugiato–Lefever equation, arising in optics. Starting from a detailed description of the stability properties of constant solutions, we then focus on the periodic steady waves which bifurcate at the onset of Turing instability. Using a centre manifold reduction, we analyse these Turing bifurcations, and prove the existence of periodic steady waves. This approach also allows us to conclude on the nonlinear orbital stability of these waves for co-periodic perturbations, i.e. for periodic perturbations which have the same period as the wave. This stability result is completed by a spectral stability result for general bounded perturbations. In particular, this spectral analysis shows that instabilities are always due to co-periodic perturbations. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.
DOI：
10.1137/16m1066221
发表时间：
2016-03
期刊：
SIAM J. Appl. Math.
影响因子：
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作者：
Rainer Mandel;W. Reichel
通讯作者：
Rainer Mandel;W. Reichel