### Abstract

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.

Original language | English |
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Pages (from-to) | 158-167 |

Number of pages | 10 |

Journal | Russian Physics Journal |

Volume | 51 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2008 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Russian Physics Journal*,

*51*(2), 158-167. https://doi.org/10.1007/s11182-008-9040-3

**Kink dynamics in the medium with a random force and dissipation in the sine-Gordon model.** / Krasnobaeva, L. A.; Shapovalov, A. V.

Research output: Contribution to journal › Article

*Russian Physics Journal*, vol. 51, no. 2, pp. 158-167. https://doi.org/10.1007/s11182-008-9040-3

}

TY - JOUR

T1 - Kink dynamics in the medium with a random force and dissipation in the sine-Gordon model

AU - Krasnobaeva, L. A.

AU - Shapovalov, A. V.

PY - 2008/2

Y1 - 2008/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=50049116312&partnerID=8YFLogxK

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U2 - 10.1007/s11182-008-9040-3

DO - 10.1007/s11182-008-9040-3

M3 - Article

VL - 51

SP - 158

EP - 167

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 2

ER -