Alexander V. Shapovalov, Roman O. Rezaev, Andrey Yu. Trifonov, “Symmetry Operators for the Fokker–Plank–Kolmogorov Equation with Nonlocal Quadratic Nonlinearity”, SIGMA, 2007, Volume 3,005, 16 pp.

This article is cited in 9 papers

Symmetry Operators for the Fokker–Plank–Kolmogorov Equation with Nonlocal Quadratic Nonlinearity

Alexander V. Shapovalov^a, Roman O. Rezaev^b, 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

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.

Keywords: symmetry operators; Fokker–Plank–Kolmogorov equation; nonlinear partial differential equations.

MSC: 35Q58; 37J15

Received: October 11, 2006; in final form December 9, 2006; Published online January 5, 2007

Language: English

DOI: 10.3842/SIGMA.2007.005