On the stability of multibreathers in Klein–Gordon chains

In this paper, a theorem, which determines the linear stability of multibreathers excited over adjacent coupled oscillators in Klein–Gordon chains, is proven. Specifically, it is shown that for soft nonlinearities, and positive nearest–neighbour 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 method can be applied to n-site breathers, where n is any finite number and provides a detailed count of the number of real and imaginary characteristic exponents of the breather, based on its configuration. In addition, an O(√(ε)) estimation of these exponents can be extracted through this procedure. 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 ε