Lie symmetry analysis and some new exact solutions of the Fokker–Planck equation

Abstract

Abstract The classical symmetry method is often employed to find precise solutions to differential equations. This method has yielded several new symmetry reductions and exact solutions for numerous theoretically and physically relevant partial differential equations. These results, as well as the symmetries of a variety of specific cases of the Fokker–Planck equation, were presented in this study using the classical Lie symmetry approach. New exact solutions to the Fokker–Planck equations are provided for each of the six cases.

Keywords

• Fokker–Planck equation
• Lie symmetry analysis
• Classical symmetries
• Determining equations
• Infinitesimal generator