Potential symmetry reduction of a convection-dispersion equation with spatial dependent water velocity

Abstract

We consider a class of a convection-dispersion equation describing the transport model of oil spilled in sea water with concentration-dependent dispersion and spatial velocity. A potential variable is introduced to the governing equation  such that the governing equation is written in conserved form (or auxiliary system). The conserved form admits a number of classical symmetries which induce potential symmetries for the governing equation. We construct group invariant solutions using admitted potential symmetries for the governing equation. The potential symmetry reduction is coupled with invariant surface condition to construct solutions via classical reduction method. The solutions are new and exact.