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SIGMA 3 (2007), 005, 16 pages math-ph/0701012
https://doi.org/10.3842/SIGMA.2007.005
Contribution to the Vadim Kuznetsov Memorial Issue
Symmetry Operators for the Fokker-Plank-Kolmogorov Equation with Nonlocal Quadratic Nonlinearity
Alexander V. Shapovalov a, Roman O. Rezaev b and Andrey Yu. Trifonov b
a) Theoretical Physics Department, Tomsk State
University, 36 Lenin Ave., 660050, Tomsk, Russia
b) Laboratory of Mathematical Physics, Mathematical
Physics Department, Tomsk Polytechnical University, 30 Lenin Ave.,
660034, Tomsk, Russia
Received October 11, 2006, in final form December 09, 2006; Published online January 05, 2007
Abstract
The Cauchy problem for the Fokker-Plank-Kolmogorov
equation with a nonlocal nonlinear drift term is reduced to a
similar problem for the correspondent linear equation. The
relation between symmetry operators of the linear and nonlinear
Fokker-Plank-Kolmogorov equations is considered. Illustrative
examples of the one-dimensional symmetry operators are presented.
Key words:
symmetry operators; Fokker-Plank-Kolmogorov equation; nonlinear partial differential equations.
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