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Travelling wave solutions for the discrete sine-Gordon equation with nonlinear pair interaction

  • C F Kreiner
  • , J Zimmer

Research output: Contribution to journal › Article › peer-review

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Abstract

The focus of study is the nonlinear discrete sine-Gordon equation, where the nonlinearity refers to a nonlinear interaction of neighbouring atoms. The existence of travelling heteroclinic, homoclinic and periodic waves is shown. The asymptotic states are chosen such that the action functional is finite. The proofs employ variational methods, in particular a suitable concentration-compactness lemma combined with direct minimisation and mountain pass arguments.
Original languageEnglish
Pages (from-to)3146-3158
Number of pages13
JournalNonlinear Analysis
Volume70
Issue number9
DOIs
Publication statusPublished - 2009

Keywords

  • Nonlinear Klein-Gordon lattice
  • Travelling waves
  • Calculus of variations
  • compactness
  • Concentration

Access to Document

  • Zimmer_NATMA_2009_90_9_3146.pdf

    NOTICE: this is the author’s version of a work that was accepted for publication in Nonlinear Analysis: Theory, Methods & Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis: Theory, Methods & Applications, Volume 70, Issue 9, 1 May 2009, DOI 10.1016/j.na.2008.04.018

    Accepted author manuscript, 263 KB

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