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An energy-based stability criterion for solitary traveling waves in Hamiltonian lattices

 

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Opened Access An energy-based stability criterion for solitary traveling waves in Hamiltonian lattices
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Author: Xu, Haitao
Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G.
Vainchtein, Anna
Coordinator/Director: J.F.R. Archilla
Department: Universidad de Sevilla. Departamento de Física Aplicada I
Date: 2017
Published in: Philosophical Transactions A, 376, 20170192-.
Document type: Article
Abstract: In this work, we revisit a criterion, originally proposed in [Nonlinearity 17, 207 (2004)], for the stability of solitary traveling 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-traveling frame, as well as at that of the Floquet problem arising when considering the traveling wave as a periodic orbit modulo a 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 traveling 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.
Cite: Xu, H., Cuevas-Maraver, J., Kevrekidis, P.G. y Vainchtein, A. (2017). An energy-based stability criterion for solitary traveling waves in Hamiltonian lattices. Philosophical Transactions A, 376, 20170192-.
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URI: http://hdl.handle.net/11441/67804

DOI: 10.1098/rsta.2017.0192

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