Demonstration of the stability or instability of multibreathers at low   coupling
  Whereas there exists a mathematical proof for one--site breathers stability, and an unpublished one for two--sites breathers, the methods for determining the stability properties of multibreathers rely in numerical computation of the Floquet multipliers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. 
J.F.R. Archilla, J. Cuevas, B. S\'anchez Rey and A. Alvarez