08-188 Renato Calleja, Yannick Sire

Travelling waves in discrete nonlinear systems with non-nearest neighbor interactions (2794K, postscript) Oct 17, 08

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. The aim of this paper is to provide a construction of travelling waves in an extended one-dimensional lattice model with non nearest neighbor interactions. These models, coming mainly from solid state physics, are known to play an important role in the mechanisms of propagation of energy. We focus on an extended version of the Klein-Gordon chains, i.e. each particle is embedded into an anharmonic potential and linearly coupled to their first and second neighbors. The technique we use is a reduction to a center manifold that goes back to \cite{sire,sirejames1,sirejames2,ioossK} and relies on the reduction of this infinite-dimensional problem to a finite-dimensional one. New phenomena appear due to the extended interactions. We find propagating solutions on the lattice which were not present for models involving coupling with only the nearest neighbors.

Files: 08-188.src( 08-188.keywords , csTWFinal2.ps )