Kink Dynamics in the Discrete Sine-Gordon System A Perturbational Approach

Abstract

Discreteness effects on dynamics of a Sine-Gordon kink in a lattice system are studied with use of a perturbation formalism due to McLaughlin and Scott. It is shown from the zeroth order condition that a kink moves in a periodic (Peierls) potential field which causes wobbling or pinning of the kink. The first order correction for the kink consists of two part, that is, a dressing part and a radiation one. The dressed kink is steeper in shape than the continuum Sine-Gordon kink and the amplitude of the backward radiation is larger than that of the forward radiation. These results are in accord with existing simulational observation.