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arXiv · 1604.06956

Energy criterion for the spectral stability of discrete breathers

Panayotis G. Kevrekidis·Jesús Cuevas-Maraver·Dmitry Pelinovsky
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Abstract

Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from the prototypical example of the Fermi-Pasta-Ulam model to Klein-Gordon nonlinear lattices, among many others. We propose a general criterion for the emergence of instabilities of discrete breathers analogous to the well-established Vakhitov-Kolokolov criterion for solitary waves. The criterion involves the change of monotonicity of the discrete breather's energy as a function of the breather frequency. Our analysis suggests and numerical results corroborate that breathers with increasing (decreasing) energy-frequency dependence are generically unstable in soft (hard) nonlinear potentials.

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Panayotis G. Kevrekidis, Jesús Cuevas-Maraver, Dmitry Pelinovsky. 2016-08-24. Energy criterion for the spectral stability of discrete breathers. https://doi.org/10.1103/physrevlett.117.094101

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