Conservation laws and associated symmetries for some classes of soil watermotion equations

We generate conservation laws of the equations that govern the motion of so il water and associate these, where possible, with Lie symmetry group gener ators in two ways. Firstly. we impose the action of any Lie-Backlund symmet ry generator on the conservation law of the soil water motion equation. Alt ernatively, we determine the conserved vectors by the direct method and the n check if the symmetry condition for the various symmetries ton the conser ved vector) is satisfied. As the equations are of evolution type, no recour se to a Lagrangian formulation is made. (C) 2001 Elsevier Science Ltd. All rights reserved.