Dynamics of sine-Gordon solitons under random perturbations: Multiplicative large-scale white noise

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Abstract
We investigate the behavior of sine-Gordon solitons under the influence of large-scale multiplicative white noise. First, we show that for the case under study the ordinary stochastic differential equations arising in stochastic perturbation theory can be solved analytically. Second, the stochastic sine-Gordon equation is simulated with an explicit algorithm we recently presented. We test the quality of stochastic perturbation theory for weak and strong noises. We show that the predictions of perturbation theory are very good for small noise intensities. For increasing noise intensities radiative damping effects lead to growing discrepancies between the simulation results and the prediction of stochastic perturbation theory.