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.
International Journal of Dynamical Systems and Differential Equations, 2009 Vol.2 No.1/2, pp.66 - 97
Published online: 02 Sep 2009 *Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article