P.G. Kevrekidis, J. Cuevas-Maraver, and D.E. Pelinovsky

Energy criterion for the spectral stability of discrete breathers

Physical Review Letters 117 (2016), 094101 (5 pages)

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 breatherís 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.

Keywords:
discrete Klein-Gordon equation, Fermi-Pasta-Ulam problem, breathers, existence and stability, small-amplitude limit.