Kink Dynamics in a Non-Autonomous Sine-Gordon Model

TL;DR

This paper develops an effective two-degree-of-freedom model for the sine-Gordon equation with space- and time-dependent parameters, accurately capturing complex kink dynamics over long times.

Contribution

It introduces a highly accurate reduced model that describes kink motion in a non-autonomous sine-Gordon system, enabling better understanding and control of soliton behavior.

Findings

The reduced model faithfully reproduces complex kink trajectories.

It remains accurate over extremely long times.

The approach facilitates improved design of soliton-based devices.

Abstract

The sine-Gordon model with space- and time-dependent parameters is considered. A highly accurate effective model with two degrees of freedom is constructed, allowing the description of the kink movement in this model even for extremely long times and nontrivial trajectories of the coherent structure. As a stringent test of the reduced order model, the case of a temporal drive leading to extremely complex kink motion is studied. The two-degree-of-freedom approximation is found to faithfully reproduce the behavior of the full field-theoretic model paving the way for both deeper understanding and improved design of soliton-based devices.