Cuevas-Maraver, JesúsKevrekidis, Panayotis G.Vainchtein, AnnaXu, Haitao2017-09-182017-09-182017Cuevas-Maraver, J., Kevrekidis, P.G., Vainchtein, A. y Xu, H. (2017). Unifying perspective: solitary traveling waves as discrete breathers in Hamiltonian lattices and energy criteria for their stability. Physical Review E, 96 (3), 032214-1-032214-9.1539-37551550-2376http://hdl.handle.net/11441/64464In 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 critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/SolitonsSolitary wavesVorticesNonlinear Dirac equationStabilityPT -symmetrySoler modelDiscrete solitonsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1103/PhysRevE.96.032214