Bifurcations from localised steady states to generalised breather solutions in the Klein-Gordon lattice (Q2380728)

Summary: We consider an infinite chain of particles linearly coupled to their nearest neighbours and look for time-periodic, spatially almost localised solutions (generalised breathers). As a starting point, we consider a time-independent breather that induces a transverse homoclinic solution of a two-dimensional recurrence relation. We can prove the existence of any finite number of (generalised) breathers which bifurcate from the time-independent breather solution at low frequency. One of the main motivations of this paper is to provide a set up, where the existence-proof of chaotic behaviour near (generalised) breathers becomes accessible to analytical methods.