Dynamics of Lattice Kinks

Abstract

In this paper we consider two models of soliton dynamics (the sine Gordon and the ϕ^4 equations) on a 1-dimensional lattice. We are interested in particular in the behavior of their kink-like solutions inside the Peierls- Nabarro barrier and its variation as a function of the discreteness parameter. We find explicitly the asymptotic states of the system for any value of the discreteness parameter and the rates of decay of the initial data to these asymptotic states. We show that genuinely periodic solutions are possible and we identify the regimes of the discreteness parameter for which they are expected to persist. We also prove that quasiperiodic solutions cannot exist. Our results are verified by numerical simulations.

50 pages, 10 figures, LaTeX document

References in corpus (4)

• Resonances, Radiation Damping and Instability in Hamiltonian Nonlinear Wave Equations
• Excitation Thresholds for Nonlinear Localized Modes on Lattices
• Nonautonomous Hamiltonians
• Metastability of Breather Modes of Time-Dependent Potentials

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