Symmetries and Self-Similar Solutions for a Generalized 2D Reaction–Diffusion Equation with Time-Dependent Coefficients

The paper investigates the Lie symmetries of a generalized nonlinear (2+1)-dimensional reaction–diffusion equation with time-dependent diffusion and reaction coefficients. The main contributions consist in the derivation of compatibility conditions that is the values of these coefficients for which the equation can be integrated. We consider the cases where the diffusion is linear in the main variable and the reaction term is a polynomial up to the fourth order, choices covering almost all models of practical interest Associated classes of self-similar solutions for these models selected via Lie compatibility conditions are highlighted. In particular, exact solutions of rational and exponential types, associated with linear, quadratic and cubic reaction terms, are mentioned.