2 Citations (Scopus)

Abstract

In this article, the Frenkel–Kontorova model for dislocation dynamics is considered, where the on-site potential consists of quadratic wells joined by small arcs, which can be spinodal (concave) as commonly assumed in physics. The existence of heteroclinic waves—making a transition from one well of the on-site potential to another—is proved by means of a Schauder fixed point argument. The setting developed here is general enough to treat such a Frenkel–Kontorova chain with smooth (C^2) on-site potential. It is shown that the method can also establish the existence of two-transition waves for a piecewise quadratic on-site potential.
LanguageEnglish
Pages2317-2342
JournalJournal of Differential Equations
Volume263
Issue number4
Early online date10 Apr 2017
DOIs
StatusPublished - 15 Aug 2017

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Traveling Wave
Dislocation Dynamics
Frenkel-Kontorova Model
Arc of a curve
Fixed point
Physics

Cite this

Travelling waves for a Frenkel-Kontorova chain. / Buffoni, Boris; Zimmer, Johannes; Schwetlick, Hartmut.

In: Journal of Differential Equations, Vol. 263, No. 4, 15.08.2017, p. 2317-2342.

Research output: Contribution to journalArticle

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