Group invariant solutions for two dimensional solute transport under realistic water flows

Abstract

We consider a form of the solute transport equation in streamline coordinates. Symmetry analysis of the equation for solute transport with realistic water flows, result in a number of admitted nontrival classical Lie point symmetries. Reduction by one of the number of variables of the governing equation are performed using members of the one dimensional optimal system. However, we construct invariant solutions using two dimensional nonabelian Lie subalgebra and other techniques.

Keywords: Solute transport, saturated soil, Lie point symmetries, analytical solutions

Quaestiones Mathematicae 29(2006), 73–83