Existence of subsonic heteroclinic waves for the Frenkel-Kontorova model with piecewise quadratic on-site potential

Carl Friedrich Kreiner; Johannes Zimmer

doi:10.1088/0951-7715/24/4/007

Existence of subsonic heteroclinic waves for the Frenkel-Kontorova model with piecewise quadratic on-site potential

Carl Friedrich Kreiner
, Johannes Zimmer

Technical University of Munich
University of Bath, Department of Mathematical Sciences

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

4 Scopus citations

Abstract

We give an existence proof for heteroclinic wave solutions to the Frenkel-Kontorova model of dislocation dynamics. The on-site potential is assumed to be piecewise quadratic. The framework employed here allows us to determine explicitly a regime of subsonic velocities for which travelling waves exist.

Original language	English
Pages (from-to)	1137-1163
Number of pages	27
Journal	Nonlinearity
Volume	24
Issue number	4
DOIs	https://doi.org/10.1088/0951-7715/24/4/007
State	Published - Apr 2011
Externally published	Yes

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10.1088/0951-7715/24/4/007

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title = "Existence of subsonic heteroclinic waves for the Frenkel-Kontorova model with piecewise quadratic on-site potential",

abstract = "We give an existence proof for heteroclinic wave solutions to the Frenkel-Kontorova model of dislocation dynamics. The on-site potential is assumed to be piecewise quadratic. The framework employed here allows us to determine explicitly a regime of subsonic velocities for which travelling waves exist.",

author = "Kreiner, \{Carl Friedrich\} and Johannes Zimmer",

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T1 - Existence of subsonic heteroclinic waves for the Frenkel-Kontorova model with piecewise quadratic on-site potential

AU - Kreiner, Carl Friedrich

AU - Zimmer, Johannes

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N2 - We give an existence proof for heteroclinic wave solutions to the Frenkel-Kontorova model of dislocation dynamics. The on-site potential is assumed to be piecewise quadratic. The framework employed here allows us to determine explicitly a regime of subsonic velocities for which travelling waves exist.

AB - We give an existence proof for heteroclinic wave solutions to the Frenkel-Kontorova model of dislocation dynamics. The on-site potential is assumed to be piecewise quadratic. The framework employed here allows us to determine explicitly a regime of subsonic velocities for which travelling waves exist.

UR - https://www.scopus.com/pages/publications/79952968068

U2 - 10.1088/0951-7715/24/4/007

DO - 10.1088/0951-7715/24/4/007

M3 - Article

AN - SCOPUS:79952968068

SN - 0951-7715

VL - 24

SP - 1137

EP - 1163

JO - Nonlinearity

JF - Nonlinearity

IS - 4

ER -

Existence of subsonic heteroclinic waves for the Frenkel-Kontorova model with piecewise quadratic on-site potential

Abstract

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