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Onset of spatiotemporal chaos in damped anharmonically driven sine-Gordon systems

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  • Chacón, R.

Abstract

The onset is demonstrated of spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping of a sinusoidal force. After introducing soliton collective coordinates, Melnikov’s method is applied to the resulting effective equation of motion to deduce the parameter-space regions of the ac force where chaotic instabilities are induced. The analysis reveals that the chaotic threshold amplitude when altering solely the pulse shape presents a minimum when the transmitted impulse is maximal, the remaining parameters being held constant. The universality of the results is shown by studying the behaviour of the Lyapunov exponent from a simple recursion relation which models an unstable limit cycle. Computer simulations of the sine-Gordon system show good agreement with the theoretical predictions. Additionally, it is found that the reshaping-induced order↔chaos route is especially rich, including transitions from a two-breather state to a spatially uniform, periodic oscillatory state. The appearance of this spatially uniform state is explained by means of geometrical resonance analysis.

Suggested Citation

  • Chacón, R., 2008. "Onset of spatiotemporal chaos in damped anharmonically driven sine-Gordon systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 902-911.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:3:p:902-911
    DOI: 10.1016/j.chaos.2006.09.084
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