Approximate Generalized Conditional Symmetries for the Perturbed Nonlinear Diffusion--Convection Equations

The concept of approximate generalized conditional symmetry (AGCS) as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit certain types of AGCSs is derived. Some approximate solutions to the resulting equations can be obtained via the AGCS and the corresponding unperturbed equations.