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.