New Solutions for Slow Moving Kinks in a Forced Frenkel-Kontorova Chain
Dynamical Systems
2015-06-05 v2 Materials Science
Mathematical Physics
math.MP
Pattern Formation and Solitons
Abstract
We construct new traveling wave solutions of moving kink type for a modified, driven, dynamic Frenkel-Kontorova model, representing dislocation motion under stress. Formal solutions known so far are inadmissible for velocities below a thresh- old value. The new solutions fill the gap left by this loss of admissibility. Analytical and numerical evidence is presented for their existence; however, dynamic simulations suggest that they are probably unstable.
Keywords
Cite
@article{arxiv.1205.3006,
title = {New Solutions for Slow Moving Kinks in a Forced Frenkel-Kontorova Chain},
author = {Phoebus Rosakis and Anna Vainchtein},
journal= {arXiv preprint arXiv:1205.3006},
year = {2015}
}
Comments
25 pages, 14 figures