Nonlocal symmetries and classes of exact solutions for a convection-dispersion model

Abstract

In this paper, we consider a form of convection-dispersion equation given in terms of the stream functions. The governing equation describing movements of contaminants under radial water flow background is given in the conserved form. As such, the conserved form of the governing equation may be written as a system of first order partial differential equations referred to as an auxiliary system, by the introduction of the nonlocal variable (or the potential variable). The resulting system of equations admits a number of (local) point symmetries which induce the nonlocal symmetries for the original governing equation. We construct classes of exact solutions using admitted genuine nonlocal symmetries, which include the invariant solutions obtained via corresponding point symmetries of the governing equation.

Keywords: Convection-dispersion equations, solute transport, nonlocal symmetries, exact solutions.