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

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