D. Pelinovsky and A. Sakovich
Multi-site breathers in Klein–Gordon lattices:
stability, resonances, and bifurcations
Nonlinearity 25 (2012) 3423–3451
Abstract:
We prove a general criterion of spectral stability of multi-site breathers in the
discrete Klein–Gordon equation with a small coupling constant. In the anticontinuum
limit, multi-site breathers represent excited oscillations at different
sites of the lattice separated by a number of ‘holes’ (sites at rest). The criterion
describes how the stability or instability of a multi-site breather depends on
the phase difference and distance between the excited oscillators. Previously,
only multi-site breathers with adjacent excited sites were considered within the
first-order perturbation theory. We showthat the stability of multi-site breathers
with one-site holes changes for large-amplitude oscillations in soft nonlinear
potentials. We also discover and study a symmetry-breaking (pitchfork)
bifurcation of one-site and multi-site breathers in soft quartic potentials near
the points of 1 : 3 resonance.
Keywords:
Discrete Klein-Gordon equation, discrete breathers, anti-continuum limit,
Floquet multipliers, pitchfork bifurcation, 1:3 resonance