Demonstration of the stability or instability of multibreathers at low coupling

Details Demonstration of the stability or instability of multibreathers at low coupling Demonstration of the stability or instability of multibreathers at low coupling

2002-08-08

arxiv.org/abs/nlin/0208014v2

Physica D, 180(3-4):235-255, 2003.

Nonlinear Sciences

Pattern Formation and Solitons

22 pages, 4 figures

Scientific paper

Whereas there exists a mathematical proof for one--site breathers stability, and an unpublished one for two--sites breathers, the methods for determining the stability properties of multibreathers rely in numerical computation of the Floquet multipliers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 Schr\"odinger 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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