Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 005, 16 pages      math-ph/0701012      http://dx.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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