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Conservation laws and invariant solutions for soil water equations

Pages: 477 - 481, Issue Special, July 2003

 Abstract        Full Text (137.9K)              

C. M. Khalique - International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, University of North-West, Private Bag X 2046, Mmabatho 2735, South Africa (email)
G. S. Pai - International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, University of North-West, Private Bag X 2046, Mmabatho 2735, South Africa (email)

Abstract: We determine conservation laws for a class of soil water equations and associate these, where possible, with Lie symmetry generators. One cannot invoke Noether’s theorem here as there is no Lagrangian for these equations. We also obtain exact solutions for such a class of equations. These solutions are invariant under a three-dimensional subalgebra of the symmetry Lie algebra.

Keywords:  Lie point symmetries, Conservation Laws, Soil Water Equations;
Mathematics Subject Classification:  Primary: 35L65, 70S10, 34C14 ; Secondary: 34C20.

Received: September 2002;      Revised: April 2003;      Published: April 2003.