Multibreather stability in discrete Klein–Gordon equations: Beyond nearest neighbor interactions

•We study multibreather stability in discrete Klein–Gordon equations.•We show stability results for coupling interactions with the second and third neighbors.•We also investigate the stability of multibreathers with nonstandard phase shifts.

We present results on multibreather stability in one-dimensional nonlinear Klein–Gordon chains. Our analysis is based on Aubryʼs band theory and perturbation theory. First, we provide an alternative proof of the stability of multibreathers in a chain with nearest neighbor interactions only. Then, we extend our analysis to the case of interactions with up to three neighbors. For next-nearest neighbor and third-nearest neighbor interactions we also extend the theory to study the stability properties of recently found multibreathers that have nonstandard phase shifts (not equal to 0 or π).