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

C F Kreiner; J Zimmer

doi:10.3934/dcds.2009.25.915

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

C F Kreiner, J Zimmer

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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.

Original language	English
Pages (from-to)	915-931
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems
Volume	25
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2009.25.915
Publication status	Published - Nov 2009

Keywords

continuum
solitary waves
Klein-Gordon lattice
travelling waves
concentration compactness

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10.3934/dcds.2009.25.915

Zimmer_DCDSA_2009_25_3_915.pdf

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title = "Heteroclinic travelling waves for the lattice sine-Gordon equation with linear pair interaction",

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 = "continuum, solitary waves, Klein-Gordon lattice, travelling waves, concentration compactness",

author = "Kreiner, {C F} and J Zimmer",

year = "2009",

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N2 - 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.

AB - 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.

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KW - solitary waves

KW - Klein-Gordon lattice

KW - travelling waves

KW - concentration compactness

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JO - Discrete and Continuous Dynamical Systems

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

Abstract

Keywords

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

Cite this