Determination of the onset of spatiotemporal complexity induced by soliton competition in a perturbed sine-Gordon chain

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Abstract
The competition between sine-Gordon-breather and kink-antikink-pair solitons under the influence of damping and both ac and dc driving is investigated. We introduce soliton collective coordinates, and develop equations of motion for this system. Then we analyze the transition by calculating the perturbed separation of the stable and unstable orbits near the homoclinic point of the motion using Melnikov’s method. We find that the threshold for complicated behavior is strongly dependent on the frequency of the ac driving, and that the contribution of the dc driving is to lower this threshold.