Nonlinear Fokker-Planck-Kolmogorov equation in the semiclassical coherent trajectory approximation

Abstract

A semiclassical asymptotic of the Cauchy problem is constructed for the two-dimensional Fokker-Planck equation with nonlocal nonlinearity in the class of trajectory concentrated functions based on the complex WKB-Maslov method. The system of Einstein-Ehrenfest equations describing the dynamics of average values of the coordinate operator and centered moments is derived. The results obtained are illustrated by a number of examples.

Original language	English
Pages (from-to)	592-604
Number of pages	13
Journal	Russian Physics Journal
Volume	48
Issue number	6
DOIs	https://doi.org/10.1007/s11182-005-0175-1
Publication status	Published - 1 Jun 2005

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1007/s11182-005-0175-1

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title = "Nonlinear Fokker-Planck-Kolmogorov equation in the semiclassical coherent trajectory approximation",

abstract = "A semiclassical asymptotic of the Cauchy problem is constructed for the two-dimensional Fokker-Planck equation with nonlocal nonlinearity in the class of trajectory concentrated functions based on the complex WKB-Maslov method. The system of Einstein-Ehrenfest equations describing the dynamics of average values of the coordinate operator and centered moments is derived. The results obtained are illustrated by a number of examples.",

author = "Bezverbnyi, {A. V.} and Gogolev, {A. S.} and Rezaev, {R. O.} and Trifonov, {A. Yu}",

year = "2005",

month = jun,

day = "1",

doi = "10.1007/s11182-005-0175-1",

language = "English",

volume = "48",

pages = "592--604",

journal = "Russian Physics Journal",

issn = "1064-8887",

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T1 - Nonlinear Fokker-Planck-Kolmogorov equation in the semiclassical coherent trajectory approximation

AU - Bezverbnyi, A. V.

AU - Gogolev, A. S.

AU - Rezaev, R. O.

AU - Trifonov, A. Yu

PY - 2005/6/1

Y1 - 2005/6/1

N2 - A semiclassical asymptotic of the Cauchy problem is constructed for the two-dimensional Fokker-Planck equation with nonlocal nonlinearity in the class of trajectory concentrated functions based on the complex WKB-Maslov method. The system of Einstein-Ehrenfest equations describing the dynamics of average values of the coordinate operator and centered moments is derived. The results obtained are illustrated by a number of examples.

AB - A semiclassical asymptotic of the Cauchy problem is constructed for the two-dimensional Fokker-Planck equation with nonlocal nonlinearity in the class of trajectory concentrated functions based on the complex WKB-Maslov method. The system of Einstein-Ehrenfest equations describing the dynamics of average values of the coordinate operator and centered moments is derived. The results obtained are illustrated by a number of examples.

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