Bifurcations from localised steady states to generalised breather solutions in the Klein-Gordon lattice
by Marc Georgi
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 2, No. 1/2, 2009

Abstract: 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.

Online publication date: Wed, 02-Sep-2009

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