Kink dynamics in the medium with a random force and dissipation in the sine-Gordon model

Within the formalism of the Fokker-Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine-Gordon model. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker-Planck equation for the momentum distribution function coincides with the equation describing the Ornstein-Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker-Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 44–51, February, 2008.