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arXiv · 1507.03189

Travelling waves for a Frenkel-Kontorova chain

Boris Buffoni·Hartmut Schwetlick·Johannes Zimmer
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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.

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Boris Buffoni, Hartmut Schwetlick, Johannes Zimmer. 2015-07-12. Travelling waves for a Frenkel-Kontorova chain. https://arxiv.org/abs/1507.03189

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