Equivalence Groups and Differential Invariants for (2+1) dimensional Nonlinear Diffusion Equation

TL;DR

This paper investigates the symmetry properties of a (2+1) dimensional nonlinear diffusion equation, deriving transformations and invariants that connect linear and nonlinear forms, and provides exact solutions for specific cases.

Contribution

It introduces a method to find equivalence transformations and differential invariants for the (2+1)D nonlinear diffusion equation, highlighting conditions for linearization.

Findings

Transformations between linear and nonlinear equations depend on generators of independent variables.

Exact solutions are obtained for certain nonlinear diffusion equations.

Differential invariants are identified and compared with direct integration results.

Abstract

(2+1) dimensional diffusion equation is considered within the framework of equivalence transformations. Generators for the group are obtained and admissible transformations between linear and nonlinear equations are examined. It is shown that transformations between linear and nonlinear equations are possible provided that the generators of independent variables depend on the dependent variable. Exact solutions for some nonlinear equations are obtained. Differential invariants related to the transformation groups are investigated and the results are compared with the direct integration method.