New Solutions for Slow Moving Kinks in a Forced Frenkel-Kontorova Chain

TL;DR

This paper introduces new traveling wave solutions for a modified Frenkel-Kontorova model that describe dislocation motion at low velocities, filling a gap in existing solutions, with evidence of their existence but potential instability.

Contribution

The paper presents novel low-velocity traveling wave solutions for a driven Frenkel-Kontorova model, expanding understanding of dislocation dynamics under stress.

Findings

New solutions exist at velocities below previous thresholds

Analytical and numerical evidence supports their existence

Simulations indicate these solutions are likely unstable

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.