An energy-based stability criterion for solitary travelling waves in Hamiltonian lattices
An energy-based stability criterion for solitary travelling waves in Hamiltonian lattices
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DOI：
10.1098/rsta.2017.0192
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发表时间：
2017-11
期刊：
影响因子：
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通讯作者：
Haitao Xu;J. Cuevas-Maraver;P. Kevrekidis;A. Vainchtein
中科院分区：
文献类型：
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作者：
Haitao Xu;J. Cuevas-Maraver;P. Kevrekidis;A. Vainchtein
在这项工作中，我们重新审视了最初在Friesecke&Pego(Friesecke&Pego 2004非线性17,207-227)中提出的准则。(DOI：0951715/10.1088/17/1/013)，研究了哈密顿无限维格子动力系统中孤立行波的稳定性。我们从稳定性理论的角度讨论了这一判据的含义，包括同行标架中超前延迟微分方程谱分析的意义，以及将行波视为周期轨道模移时产生的Floquet问题的意义。我们建立了相应本征值和Floquite乘子的对应关系，并给出了它们对临界点附近行波速度的依赖关系的显式表达式。数值结果被用来证实两个不同模型中的相关预测，其中稳定性可能发生两次变化。文中还讨论了本研究的扩展、概括和未来的发展方向。本文是“非线性波和花样的稳定性及相关问题”主题的一部分。
In this work, we revisit a criterion, originally proposed in Friesecke & Pego (Friesecke & Pego 2004 Nonlinearity 17, 207–227. (doi:10.1088/0951715/17/1/013)), for the stability of solitary travelling waves in Hamiltonian, infinite-dimensional lattice dynamical systems. We discuss the implications of this criterion from the point of view of stability theory, both at the level of the spectral analysis of the advance-delay differential equations in the co-travelling frame, as well as at that of the Floquet problem arising when considering the travelling wave as a periodic orbit modulo shift. We establish the correspondence of these perspectives for the pertinent eigenvalue and Floquet multiplier and provide explicit expressions for their dependence on the velocity of the travelling wave in the vicinity of the critical point. Numerical results are used to corroborate the relevant predictions in two different models, where the stability may change twice. Some extensions, generalizations and future directions of this investigation are also discussed. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.