DC motion of ac driven sine-Gordon solitons

TL;DR

This paper demonstrates that pure ac driving can induce a net dc motion of sine-Gordon solitons, with the velocity depending on the driving phase, confirmed by both analytical and numerical methods.

Contribution

It provides the first comprehensive analysis showing ac driving can produce dc soliton motion in the sine-Gordon model, resolving a long-standing question.

Findings

Ac driving induces a net dc velocity in sine-Gordon solitons.

The velocity depends on the phase of the ac drive.

Numerical simulations confirm the analytical predictions.

Abstract

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.