Heir-Equations Method and Non-Classical Symmetries of Cahn-Allen and Fokker-Planck Equations

Abstract

The main goal of this work is to determine the exact solutions to the Fokker-Planck and Cahn-Allen equations by using the heir-equations method. The heir-equations approach is a novel and efficient way to identify symmetries that are nonclassical. According to M.C. Nucci's research, the method initially provides an iteration process over the nonclassical symmetry of a given equation to obtain a class of nonlinear equations that inherit its Lie symmetry characteristics. The method especially provides more successful results when applying evolutionary-type partial differential equations. The proposed method successfully derives nonclassical symmetries and their corresponding exact solutions for both equations.