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Demonstration of the stability or instability of multibreathers at low coupling

J. F. R. Archilla·J. Cuevas·B. Sánchez Rey·A. Alvarez
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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Whereas there exists a mathematical proof for one--site breathers stability, and an unpublished one for two--sites breathers, the methods for determining the stability properties of multibreathers rely in numerical computation of the Floquet multipliers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.

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J. F. R. Archilla, J. Cuevas, B. Sánchez Rey, A. Alvarez. 2003-02-09. Demonstration of the stability or instability of multibreathers at low coupling. https://doi.org/10.1016/s0167-2789(03)00064-2

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