Oscillatory wave fronts in chains of coupled nonlinear oscillators

Abstract

Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress $F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate, for $F_{cd}<|F|<F_{cs}$ stable static and moving wave fronts coexist, and for $|F|>F_{cs}$ (static Peierls stress) there are only stable moving wave fronts. For piecewise linear models, extending an exact method of Atkinson and Cabrera's to chains with damped dynamics corroborates this description. For smooth nonlinearities, an approximate analytical description is found by means of the active point theory. Generically for small or zero damping, stable wave front profiles are non-monotone and become wavy (oscillatory) in one of their tails.

18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev. E

References in corpus (4)

• Propagation failure of traveling waves in a discrete bistable medium
• Moving lattice kinks and pulses: an inverse method
• Wavefront depinning transition in discrete one-dimensional reaction-diffusion systems
• Motion of Wavefronts in Semiconductor Superlattices

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• Propagation of transition front in bi-stable nondegenerate chains: model dependence and universality
• New Solutions for Slow Moving Kinks in a Forced Frenkel-Kontorova Chain
• Front propagation in lattices with on-site bistable non-degenerate potential: multiplicity, bifurcations and route to chaos
• Stability of traveling waves in a driven Frenkel-Kontorova model
• A Family of Solitary Waves in Frenkel-Kontorova Lattice