We prove the existence of monoparametric families of multibreathers in chains of Hamiltonian oscillators of one degree of freedom, with the total energy of the chain as a parameter. At the same time we evaluate the neighborhood of the initial conditions for these solutions, as well as their stability. For the proof we use an idea originally proposed by Poincaré. We apply our results to calculate families of multibreathers in a chain consisting of coupled Morse oscillators.

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The twist condition is a necessary condition in integrable Hamiltonian systems and symplectic maps to obtain Poincaré–Birkhoff bifurcations under small perturbations. When this condition does not hold, topological structures other than Poincaré–Birkhoff chains arise in phase space through bifurcations of isolated periodic orbits and reconnections of asymptotic manifolds. In this paper we construct an integrable model Hamiltonian with degeneracies suitable to observe these phenomena close to nontwist resonant tori. The generation of isochronous chains and the stability of their fixed points is determined analytically and a condition for the reconnection is found. Particular examples are given, illustrating the bifurcation and reconnection scenario for several cases of degeneracy.

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In the present article we present general linear stability criteria for multibreathers in Klein–Gordon chains at low coupling. Our method is constructive, which means that provided a specific potential the method provides the allowed multibreathers and their characteristic exponent to leading order of approximation.

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