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

Pages: 915 - 931, Volume 25, Issue 3, November 2009

doi:10.3934/dcds.2009.25.915       Abstract        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.