Symmetry reductions of a nonlinear convection-dispersion model arising in contaminant transport theory

In this paper we consider a nonlinear convection-dispersion equation arising in contaminant transport. The water flow velocity is considered to be spatially-dependent and dispersion coefficient depends on concentration. A direct group classification resulted in a number of cases for which the governing equation admits Lie point symmetries. In each case the one dimensional optimal system of subalgebras is constructed. Reductions are performed. The reduced ordinary differential equations (ODEs) are nonlinear and difficult to solve exactly. On the other hand we consider the steady state problem and applied the method of canonical coordinates to determine exact solutions.