Heteroclinic travelling waves for the lattice sine-Gordon        equation with linear pair interaction

Carl-Friedrich Kreiner; Johannes Zimmer

doi:10.3934/dcds.2009.25.915

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2009, Volume 25, Issue 3: 915-931. Doi: 10.3934/dcds.2009.25.915

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Heteroclinic travelling waves for the lattice sine-Gordon equation with linear pair interaction

Carl-Friedrich Kreiner^1, and
Johannes Zimmer^2,

1.
Laboratoire de mécanique des solides, École Polytechnique, 91128 Palaiseau Cedex
2.
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY

Received: April 30, 2008

Revised: February 28, 2009

Published: August 2009

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Abstract

The existence of travelling heteroclinic waves for the sine-Gordon lattice is proved for a linear interaction of neighbouring atoms. The asymptotic states are chosen such that the action functional is finite. The proof relies on a suitable concentration-compactness argument, which can be shown to hold even though the associated functional has no sub-additive structure.

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Mathematics Subject Classification: Primary: 37K60, 74J30; Secondary: 34A34.

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