Travelling lattice waves in a toy model of Lennard-Jones interaction

Christine R. Venney, Johannes Zimmer

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Abstract

We consider an infinite lattice model, where particles interact with nearest neighbour (NN) and next-to-nearest neighbours (NNN); the NN and NNN springs act against each other to mimic the Lennard-Jones potential. The existence of subsonic waves homoclinic to exponentially small periodic oscillations is shown as well as the existence of supersonic periodic solutions. The proofs rely on methods from normal form and centre space analysis for the homoclinic solutions and centre manifold analysis for the periodic solutions.
Original languageEnglish
Pages (from-to)65-84
Number of pages20
JournalQuarterly of Applied Mathematics
Volume72
Issue number1
Early online date13 Nov 2013
DOIs
Publication statusPublished - 1 Mar 2014

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