dc motion of ac driven sine-Gordon solitons

Abstract

We investigate the dependence of dc soliton motion sustained by pure ac driving in the sine-Gordon model on various parameter problems, such as frequency, initial kink velocity or relative phase. We show by means of the collective coordinate formalism that ac driving induces a net dc velocity whose modulus and direction depend on the driving phase and on the kink initial velocity. Numerical simulations of the full sine-Gordon equation confirm the correctness and accuracy of this prediction. Nontrivial cases when dc soliton motion is transformed into oscillation as well as the effects of damping are analyzed. Our results generalize previous work on the undamped problem, and clarify a long standing issue about the existence and characteristics of this phenomenon in damped problems, whose possible appearance in other systems is also discussed.