# American Institute of Mathematical Sciences

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

 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.
Citation: Carl-Friedrich Kreiner, Johannes Zimmer. Heteroclinic travelling waves for the lattice sine-Gordon equation with linear pair interaction. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 915-931. doi: 10.3934/dcds.2009.25.915
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