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

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.

25 pages, 14 figures

References in corpus (2)

• Oscillatory wave fronts in chains of coupled nonlinear oscillators
• Direct experimental measurement of the speed-stress relation for dislocations in a plasma crystal

Cited by in corpus (5)

• A One-Dimensional Peridynamic Model of Defect Propagation and its Relation to Certain Other Continuum Models
• Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials
• Stability of traveling waves in a driven Frenkel-Kontorova model
• Front propagation in lattices with on-site bistable non-degenerate potential: multiplicity, bifurcations and route to chaos
• A dislocation-dipole in one dimensional lattice model