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Unifying perspective: solitary traveling waves as discrete breathers in Hamiltonian lattices and energy criteria for their stability

Opened Access Unifying perspective: solitary traveling waves as discrete breathers in Hamiltonian lattices and energy criteria for their stability

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Autor: Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G.
Vainchtein, Anna
Xu, Haitao
Coordinador/Director: Rodríguez Archilla, Juan Francisco
Departamento: Universidad de Sevilla. Departamento de Física Aplicada I
Fecha: 2017
Tipo de documento: Artículo
Resumen: In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H(c0) evaluated at the critic...
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Tamaño: 285.8Kb
Formato: PDF

URI: http://hdl.handle.net/11441/64464

DOI: 10.1103/PhysRevE.96.032214

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