Demonstration of the stability or instability of multibreathers at low coupling

Abstract

Whereas there exists a mathematical proof for one--site breathers stability, and an unpublished one for two--sites breathers, the methods for determining the stability properties of multibreathers rely in numerical computation of the Floquet multipliers or in the weak nonlinearity approximation leading to discrete non--linear Schrödinger equations. Here we present a set of multibreather stability theorems (MST) that provides with a simple method to determine multibreathers stability in Klein--Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry's band theory. We illustrate them with several examples.

22 pages, 4 figures

References in corpus (3)

• Standing wave instabilities in a chain of nonlinear coupled oscillators
• Dark breathers in Klein-Gordon lattices. Band analysis of their stability properties
• Breathers in a system with helicity and dipole interaction

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