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

Abstract

We prove the most general theorem about spectral stability of multi-site breathers in the discrete Klein-Gordon equation with a small coupling constant. In the anti-continuum limit, multi-site breathers represent excited oscillations at different sites of the lattice separated by a number of "holes" (sites at rest). The theorem 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 show that the stability of multi-site breathers with one-site holes change 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.

34 pages, 12 figures

References in corpus (2)

• Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation
• Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain

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