Travelling waves for a Frenkel-Kontorova chain
Dynamical Systems
2015-07-14 v1
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 () 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.
Keywords
Cite
@article{arxiv.1507.03189,
title = {Travelling waves for a Frenkel-Kontorova chain},
author = {Boris Buffoni and Hartmut Schwetlick and Johannes Zimmer},
journal= {arXiv preprint arXiv:1507.03189},
year = {2015}
}