KINKS IN THE PRESENCE OF RAPIDLY VARYING PERTURBATIONS

The dynamics of sine-Gordon kinks in the presence of rapidly varying p eriodic perturbations of different physical origins is described analy tically and numerically. The analytical approach is based on asymptoti c expansions, and it allows one to derive, in a rigorous way, an effec tive nonlinear equation for the slowly varying field component in any order of the asymptotic procedure as expansions in the small parameter omega-1, omega being the frequency of the rapidly varying ac driving force. Three physically important examples of such a dynamics, i.e., k inks driven by a direct or parametric ac force, and kinks on a rotatin g and oscillating background, are analyzed in detail. It is shown that in the main order of the asymptotic procedure the effective equation for the slowly varying field component is a renormalized sine-Gordon e quation in the case of the direct driving force or rotating (but phase locked to an external ac force) background, and it is the double sine -Gordon equation for the parametric driving force. The properties of t he kinks described by the renormalized nonlinear equations are analyze d, and it is demonstrated analytically and numerically which kinds of physical phenomena may be expected in dealing with the renormalized, r ather than the unrenormalized, nonlinear dynamics. In particular, we p redict several qualitatively new effects which include, e.g., the pert urbation-induced internal oscillations of the 2pi kink in a parametric ally driven sine-Gordon model, and the generation of kink motion by a pure ac driving force on a rotating