Invariant solutions and conservation laws for soil water redistribution and extraction flow models

Abstract

In this dissertation we use Lie symmetry analysis to obtain invariant solutions for certain soil water equations. These solutions are invariant under two-parameter symmetry groups obtained by the group classification of the governing equation. We also obtain all nontrivial conservation laws for a class of (2+1) nonlinear evolution partial differential equations which are related to the soil water equations. It is shown that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. We note that one cannot invoke Noether's theorem here as there is no Lagrangian for these partial differential equations.