Approximate potential symmetries for partial differential equations

Abstract

The method of approximate potential symmetries for partial differential equations with a small parameter is introduced. By writing a given perturbed partial differential equation R in a conserved form, an associated system S with potential variables as additional variables is obtained. Approximate Lie point symmetries admitted by S induce approximate potential symmetries of R. As applications of the theory, approximate potential symmetries for a perturbed wave equation with variable wave speed and a nonlinear diffusion equation with perturbed convection terms are obtained. The corresponding approximate group-invariant solutions are also derived.