Kink dynamics in a non-autonomous sine-Gordon model

The sine-Gordon model with space- and time-dependent parameters is considered. A highly accurate effective model with two degrees of freedom is constructed, enabling 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 an 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.