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

A. V. Bezverbnyi, A. S. Gogolev, R. O. Rezaev, A. Yu Trifonov

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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

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ASJC Scopus subject areas

Physics and Astronomy(all)

Cite this

Bezverbnyi, A. V., Gogolev, A. S., Rezaev, R. O., & Trifonov, A. Y. (2005). Nonlinear Fokker-Planck-Kolmogorov equation in the semiclassical coherent trajectory approximation. Russian Physics Journal, 48(6), 592-604. https://doi.org/10.1007/s11182-005-0175-1

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AU - Trifonov, A. Yu

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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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10.1007/s11182-005-0175-1