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September  2009, 25(3): 915-931. doi: 10.3934/dcds.2009.25.915

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, France
2. 

Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom

Received  May 2008 Revised  March 2009 Published  August 2009

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.
Keywords: concentration compactness., Klein-Gordon lattice, travelling waves.
Mathematics Subject Classification: Primary: 37K60, 74J30; Secondary: 34A3.
Citation: Carl-Friedrich Kreiner, Johannes Zimmer. Heteroclinic travelling waves for the lattice sine-Gordon equation with linear pair interaction. Discrete & Continuous Dynamical Systems, 2009, 25 (3) : 915-931. doi: 10.3934/dcds.2009.25.915
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