
This article is cited in 1 scientific paper (total in 1 paper)
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
coarsegrained 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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Theoretical and Mathematical Physics, 1984, 59:1, 396–403
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Received: 21.06.1983
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
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\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 117128
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\mathscinet{http://www.ams.org/mathscinetgetitem?mr=749009}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 59
\issue 1
\pages 396403
\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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http://mi.mathnet.ru/eng/tmf4780 http://mi.mathnet.ru/eng/tmf/v59/i1/p117
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V. V. Sokolov, “Quasienergy integral for canonical maps”, Theoret. and Math. Phys., 67:2 (1986), 464–473

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