SG-kink dynamics under dissipation and external regular and random forces

L. A. Krasnobaeva, A. V. Shapovalov

Research output: Chapter in Book/Report/Conference proceedingChapter


Within the formalism of the Fokker-Planck equation, the influence of nonstationaryregular external force, random force, and dissipation on the kink dynamics is investigatedin the sine-Gordon model. The evolution equation of the kink momentum is written inthe form of the stochastic differential equation in the Stratonovich sense within theframework of the well-known McLaughlin and Scott energy approach. Thecorresponding Fokker-Planck equation for the momentum distribution function coincideswith the equation describing the Ornstein-Uhlenbek process with a regular nonstationaryexternal force. The influence of the nonlinear stochastic effects on the kink dynamics isdescribed in terms of the nonlinear Fokker-Planck equation with the drift coefficientdependent on the first moment of the distribution function. Exact solutions of both linearand nonlinear Fokker-Planck equations are presented. The average value and the varianceof the kink momentum are obtained in explicit form using the above exact solutions.Examples are considered which demonstrate the influence of the external regular andrandom forces on the evolution of the average value and variance of the kink momentum.

Original languageEnglish
Title of host publicationMathematical Models of Non-linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere
PublisherNova Science Publishers Inc
Number of pages14
ISBN (Print)9781608769940
Publication statusPublished - 2013
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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