DC motion of ac driven sine-Gordon solitons

We investigate the possibility of dc soliton motion sustained by pure ac driving in the sine-Gordon model. 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. Numerical simulations of the full sine-Gordon equation confirm the correctness and accuracy of this prediction. Non trivial cases when dc soliton motion is transformed into oscillatory as well as the effects of damping are analyzed. Our results settle a long standing issue about the existence and characteristics of this phenomenon, whose possible appearance in other systems is also discussed.