ac driven sine-Gordon solitons: dynamics and stability

TL;DR

This paper provides a comprehensive analytical and numerical study of ac driven sine-Gordon solitons, clarifying their motion and stability, and resolving controversies about their behavior under different force and damping conditions.

Contribution

It offers the first full analytical and numerical characterization of soliton dynamics and stability in ac driven sine-Gordon systems, including the effects of damping and force parameters.

Findings

Kink solitons exhibit dc or oscillatory motion depending on initial velocity and force parameters.

Damping prevents dc motion of solitons.

Breathers do not exhibit dc motion and have a specific existence range for force amplitude.

Abstract

The ac driven sine-Gordon equation is studied analytically and numerically, with the aim of providing a full description of how soliton solutions behave. To date, there is much controversy about when ac driven dc motion is possible. Our work shows that kink solitons exhibit dc or oscillatory motion depending on the relation between their initial velocity and the force parameters. Such motion is proven to be impossible in the presence of damping terms. For breathers, the force amplitude range for which they exist when dissipation is absent is found. All the analytical results are compared with numerical simulations, which in addition exhibit no dc motion at all for breathers, and an excellent agreement is found. In the conclusion, the generality of our results and connections to others systems for which a similar phenomenology may arise are discussed.