Similarity Solutions of a Class of Perturbative Fokker-Planck Equation

TL;DR

This paper investigates similarity solutions for a specific class of Fokker-Planck equations with constant diffusion and small time-dependent drift, using the similarity method to find solutions with scaling properties.

Contribution

It extends previous work by applying the similarity method to find solutions with scaling behavior for this class of Fokker-Planck equations.

Findings

Derived similarity solutions with scaling properties.

Established the connection between Fokker-Planck and Schrödinger equations.

Demonstrated the applicability of the similarity method to this class.

Abstract

In a previous work, a perturbative approach to a class of Fokker-Planck equations, which have constant diffusion coefficients and small time-dependent drift coefficients, was developed by exploiting the close connection between the Fokker-Planck equations and the Schrodinger equations. In this work, we further explore the possibility of similarity solutions of such a class of Fokker-Planck equations. These solutions possess definite scaling behaviors, and are obtained by means of the so-called similarity method.