Conservation laws and invariant solutions for soil water equations

C. M. Khalique; G. S. Pai

doi:10.3934/proc.2003.2003.477

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2003, Volume 2003: 477-481. Doi: 10.3934/proc.2003.2003.477 open access

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Conservation laws and invariant solutions for soil water equations

C. M. Khalique^1, and
G. S. Pai^1,

1.
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, University of North-West, Private Bag X 2046, Mmabatho 2735

Received: August 31, 2002

Revised: March 31, 2003

Published: March 2003

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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.

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Mathematics Subject Classification: Primary: 35L65, 70S10, 34C14 ; Secondary: 34C20.

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