Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


Authors: Christine R. Venney and Johannes Zimmer
Journal: Quart. Appl. Math. 72 (2014), 65-84
MSC (2010): Primary 37L10, 82C20
Published electronically: November 13, 2013
MathSciNet review: 3185132
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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.


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Additional Information

Christine R. Venney
Affiliation: Dept. of Mathematical Sciences, University of Bath, Bath, U. K.

Johannes Zimmer
Affiliation: Dept. of Mathematical Sciences, University of Bath, Bath, U. K.

DOI: https://doi.org/10.1090/S0033-569X-2013-01320-4
Received by editor(s): February 25, 2012
Published electronically: November 13, 2013
Article copyright: © Copyright 2013 Brown University


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