D. Pelinovsky and A. Sakovich

Multi-site breathers in Klein–Gordon lattices: stability, resonances, and bifurcations

Nonlinearity 25 (2012) 3423–3451

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.

Discrete Klein-Gordon equation, discrete breathers, anti-continuum limit, Floquet multipliers, pitchfork bifurcation, 1:3 resonance