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).