Group analysis of a class of nonlinear Kolmogorov equations

TL;DR

This paper performs a comprehensive Lie symmetry analysis of a class of nonlinear Kolmogorov equations with time-dependent coefficients, identifying symmetries and classifications to facilitate solution methods.

Contribution

It provides a complete group classification of (1+2)-dimensional nonlinear Kolmogorov equations using gauge transformations and equivalence groups.

Findings

Complete group classification achieved.

Identification of optimal gauge choices.

Application of equivalence transformations to simplify analysis.

Abstract

A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group classification is achieved using a gauging of arbitrary elements (i.e. via reducing the number of variable coefficients) with the application of equivalence transformations. Two possible gaugings are discussed in detail in order to show how equivalence groups serve in making the optimal choice.