Group classification of a class of generalized nonlinear Kolmogorov equations and exact solutions

TL;DR

This paper performs a group classification of a broad class of generalized nonlinear Kolmogorov equations using Lie symmetries, and finds exact solutions with maximal symmetry properties.

Contribution

It provides the first comprehensive group classification of these equations and derives new exact solutions based on symmetry analysis.

Findings

Classification of Lie symmetries for the equations

Identification of equations with maximal symmetry

Derivation of exact solutions for these equations

Abstract

A class of generalized nonlinear Kolmogorov equations is investigated. We present the group classification of Lie symmetries of the class with respect to the group of equivalence transformations. We find a number of exact solutions of nonlinear Kolmogorov equations which has the maximal symmetry properties.