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

C F Kreiner, J Zimmer

Research output: Contribution to journalArticle

9 Citations (Scopus)
140 Downloads (Pure)

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: Theory Methods & Applications
Volume70
Issue number9
DOIs
Publication statusPublished - 2009

Keywords

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

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