Travelling waves for a Frenkel-Kontorova chain

Boris Buffoni, Johannes Zimmer, Hartmut Schwetlick

Research output: Contribution to journalArticle

2 Citations (Scopus)
119 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)2317-2342
Number of pages26
JournalJournal of Differential Equations
Volume263
Issue number4
Early online date10 Apr 2017
DOIs
Publication statusPublished - 15 Aug 2017

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  • Projects

    Wolfson Merit Award - Non equilibrium Particles & PDE

    Zimmer, J.

    The Royal Society

    1/05/1630/04/21

    Project: Research council

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