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 TMF, 1984, Volume 59, Number 1, Pages 117–128 (Mi tmf4780)

Moments of the distributio function and kinetic equation for stochastic motion of a nonlinear oscillator

V. V. Sokolov

Abstract: An analytic approach to study of the stochastic motion of a nonlinear system in a periodic external potential is developed. In contrast to a number of other approaches, no additional external random parameters are introduced a priori. A method for calculating the moments of the distribution function is constructed. In particular, the problem of calculating the diffusion coefficient is reduced to the solution of an infinite inhomogeneous system of linear equations. In the limit of large values of Chirikov's stochasticity parameter $K$, this system simplifies strongly and reduces to a system of two equations up to terms of order $1/\sqrt{4K}$. In this limit, the diffusion coefficient can be readily found in explicit form. In the leading approximation in the parameter $1/\sqrt{4K}$ a closed expression is obtained for the generating function of the moments of the distribution function. It differs strongly from the standard Gauss[an expression. A kinetic equation is obtained for the coarse-grained distribution function. Although it differs from the standard diffusion equation that is generally used, its solution tends asymptotically at large times to the Gaussian distribution.

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English version:
Theoretical and Mathematical Physics, 1984, 59:1, 396–403

Bibliographic databases:

Citation: V. V. Sokolov, “Moments of the distributio function and kinetic equation for stochastic motion of a nonlinear oscillator”, TMF, 59:1 (1984), 117–128; Theoret. and Math. Phys., 59:1 (1984), 396–403

Citation in format AMSBIB
\Bibitem{Sok84} \by V.~V.~Sokolov \paper Moments of the distributio function and kinetic equation for stochastic motion of a nonlinear oscillator \jour TMF \yr 1984 \vol 59 \issue 1 \pages 117--128 \mathnet{http://mi.mathnet.ru/tmf4780} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=749009} \transl \jour Theoret. and Math. Phys. \yr 1984 \vol 59 \issue 1 \pages 396--403 \crossref{https://doi.org/10.1007/BF01028518} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984TR03500009} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. V. Sokolov, “Quasienergy integral for canonical maps”, Theoret. and Math. Phys., 67:2 (1986), 464–473
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