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

C F Kreiner, J Zimmer

Research output: Contribution to journalArticle

8 Citations (Scopus)
66 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

Fingerprint

sine-Gordon equation
Concentration-compactness
Mountain Pass
Periodic Wave
Sine-Gordon Equation
Nonlinear Interaction
Homoclinic
Discrete Equations
Traveling Wave Solutions
Variational Methods
Lemma
Nonlinearity
Atoms
Interaction

Keywords

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

Cite this

Travelling wave solutions for the discrete sine-Gordon equation with nonlinear pair interaction. / Kreiner, C F; Zimmer, J.

In: Nonlinear Analysis: Theory Methods & Applications, Vol. 70, No. 9, 2009, p. 3146-3158.

Research output: Contribution to journalArticle

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