On the stability of multibreathers in Klein-Gordon chains

TL;DR

This paper proves a theorem determining the linear stability of multibreathers in Klein-Gordon chains, showing how stability depends on nonlinearity type, coupling sign, and phase relations, with numerical validation.

Contribution

It introduces a theorem that predicts multibreather stability based on nonlinearity and coupling, applicable to any finite number of sites, with quantitative estimates and numerical confirmation.

Findings

Stable structures depend on nonlinearity type and coupling sign.

Numerical simulations agree with theoretical predictions for small coupling.

The theorem applies to any finite number of sites in the chain.

Abstract

In the present paper, a theorem, which determines the linear stability of multibreathers in Klein-Gordon chains, is proven. Specifically, it is shown that for soft nonlinearities, and positive inter-site coupling, only structures with adjacent sites excited out-of-phase may be stable, while only in-phase ones may be stable for negative coupling. The situation is reversed for hard nonlinearities. This theorem can be applied in $n$-site breathers, where $n$ is any finite number and provides an $\cal{O}(\sqrt{\epsilon})$ estimation of the characteristic exponents of the solution. To complement the analysis, we perform numerical simulations and establish that the results are in excellent agreement with the theoretical predictions, at least for small values of the coupling constant $\epsilon$.