Abstract
We test the soundness of stochastic perturbation theory in the case of large-scale random perturbations of sine-Gordon solitons. To this end both the stochastic sine-Gordon equation and the stochastic perturbation theory equations are solved numerically. For the former we develop an explicit numerical scheme to integrate randomly perturbed nonlinear wave equations. The method is shown to work very efficiently, allowing a substantial improvement in the quality of the simulations. In the case under study, the predictions of the perturbation analysis are in good agreement with the numerical computations of the sine-Gordon equation.
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