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

C F Kreiner; J Zimmer

doi:10.1016/j.na.2008.04.018

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

11 Citations (SciVal)

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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 language	English
Pages (from-to)	3146-3158
Number of pages	13
Journal	Nonlinear Analysis: Theory Methods & Applications
Volume	70
Issue number	9
DOIs	https://doi.org/10.1016/j.na.2008.04.018
Publication status	Published - 2009

Keywords

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

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10.1016/j.na.2008.04.018

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

Cite this

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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.",

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AB - 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.

KW - Nonlinear Klein-Gordon lattice

KW - Travelling waves

KW - Calculus of variations

KW - compactness

KW - Concentration

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

Abstract

Keywords

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MATHEMATICAL ANALYSIS OF OF THE STATIC AND DYNAMIC BEHAVIOUR OF MATERIALS - ADVANCED RESEARCH FELLOWSHIP

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

Abstract

Keywords

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MATHEMATICAL ANALYSIS OF OF THE STATIC AND DYNAMIC BEHAVIOUR OF MATERIALS - ADVANCED RESEARCH FELLOWSHIP

Cite this