doi:10.3934/dcds.2009.25.915          Full text: (301.8K)

Carl-Friedrich Kreiner - Laboratoire de mécanique des solides, École Polytechnique, 91128 Palaiseau Cedex, France (email)

Johannes Zimmer - Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom (email)

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.

Keywords: Klein-Gordon lattice, travelling waves, concentration compactness.
Mathematics Subject Classification: Primary: 37K60, 74J30; Secondary: 34A34.

Received:   May   2008;   Revised:   March  2009;   Published:   August  2009.

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