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)

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.

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