Reshaping-induced spatiotemporal chaos in driven, damped sine-Gordon systems

TL;DR

This paper demonstrates how reshaping an ac force can induce spatiotemporal chaos in driven, damped sine-Gordon systems, with theoretical predictions validated by computer simulations.

Contribution

It introduces a method to control chaos in sine-Gordon systems by reshaping the driving force and applies Melnikov's method to predict chaos thresholds.

Findings

Chaos arises from competition between soliton types.

Chaos-order threshold is sensitive to force shape.

Simulations confirm theoretical predictions.

Abstract

Spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov's method is applied to the resulting effective equation of motion to estimate the parameter-space regions of the ac force where homoclinic bifurcations are induced. The analysis reveals that the chaos-order threshold exhibits sensitivity to small changes in the force shape. Computer simulations of the sine-Gordon system show good agreement with these theoretical predictions.