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Breathers in Inhomogeneous Nonlinear Lattices: an Analysis via Centre Manifold Reduction by James, Guillaume; Sanchez-Rey, Bernardo; Cuevas, Jesus is a scholarly article available to read on EtoBox.

What is Breathers in Inhomogeneous Nonlinear Lattices: an Analysis via Centre Manifold Reduction about?

We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is reformulated as a nonautonomous recurrence in a space of time-periodic functions, where the dynamics is considered along the discrete spatial coordinate. We show that small amplitude oscillations are determined by finite-dimensional nonautonomous mappings, whose dimension depends on the solutions frequency. We consider the case of two-dimensional reduced mappings, which occurs for frequencies close to the edges of the phonon band. For an homogeneous chain, the reduced map is autonomous and reversible, and bifurcations of reversible homoclinics or heteroclinic solutions are found for appropriate parameter values. These orbits correspond respectively to discrete breathers, or dark breathers superposed on a spatially extended standing wave. Breather existence is shown in some cases for any value of the coupling constant, which generalizes an existence result obtained by MacKay and Aubry at small coupling. For an inhomogeneous chain the study of the

Author

James, Guillaume; Sanchez-Rey, Bernardo; Cuevas, Jesus

Published

2007

Language

EN