Title: Bifurcations from localised steady states to generalised breather solutions in the Klein-Gordon lattice

Authors: Marc Georgi

Addresses: Institute of Mathematics I, Freie Universitat Berlin, Arnimallee 7, 14195 Berlin, Germany

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.

Keywords: lattice differential equations; ill-posed recurrence relation; discrete breathers; centre stable manifold; chaotic behaviour; bifurcations; localised steady states; particle chains; transverse homoclinic solution.

DOI: 10.1504/IJDSDE.2009.028036

International Journal of Dynamical Systems and Differential Equations, 2009 Vol.2 No.1/2, pp.66 - 97

Published online: 02 Sep 2009 *

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