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Mathematical Problems in Engineering
Volume 2005, Issue 1, Pages 141-150
http://dx.doi.org/10.1155/MPE.2005.141

Conservation laws for equations related to soil water equations

1International Institute for Symmetry Analysis and Mathematical Modelling and Department of Mathematical Sciences, North West University, Private Bag X2046, Mmabatho 2735, South Africa
2Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa

Received 10 April 2003; Revised 7 May 2004

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We 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 also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.