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

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.15 pages