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Kink dynamics in a non-autonomous sine-Gordon model.

Tomasz Dobrowolski¹, Jacek Gatlik², Zofia Bryłowska²

¹Department of Physics and Applied Mathematics, University of the National Education Commission in Krakow, Podchora̧żych 2, 30-084 Cracow, Poland.

Chaos (Woodbury, N.Y.)

|October 17, 2025

Summary

This summary is machine-generated.

A new two-degree-of-freedom model accurately describes complex kink motion in the sine-Gordon model. This effective model aids in understanding and designing soliton-based devices.

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Area of Science:

Nonlinear dynamics
Theoretical physics
Condensed matter physics

Background:

The sine-Gordon model is a fundamental tool for studying solitons.
Understanding complex kink dynamics is crucial for soliton-based applications.
Existing models may struggle with long-term simulations and non-trivial trajectories.

Purpose of the Study:

To develop a highly accurate, reduced-order model for the sine-Gordon model with space- and time-dependent parameters.
To enable the description of kink movement over extremely long times.
To analyze complex kink trajectories and motions induced by temporal drives.

Main Methods:

Construction of an effective model with two degrees of freedom.
Analysis of kink movement and coherent structure trajectories.
Testing the reduced-order model against the full field-theoretic model under temporal drive conditions.

Main Results:

A two-degree-of-freedom effective model was successfully constructed.
The model accurately describes kink movement for long times and nontrivial trajectories.
The approximation faithfully reproduces the behavior of the full field-theoretic model, even for complex motions.

Conclusions:

The developed two-degree-of-freedom model provides a computationally efficient and accurate approach to studying the sine-Gordon model.
This work facilitates a deeper understanding of soliton dynamics.
The findings pave the way for improved design and application of soliton-based devices.