Non-classical and potential symmetry analysis of Richard's equation for moisture flow in soil

Journal of Physics A: Mathematical and General

Volumn 37, Issue 3, 2004, Pages 823-839

  Wiltshire, Ron ^a   El Kafri, Manal ^a  

^a UNIVERSITY OF GLAMORGAN   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0742305888     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/3/019     Document Type: Review

References (15)

1. Philip J R 1988 Quasi-analytic and analytic approaches to unsaturated flow Flow and Transport in the Natural Environment: Advances and Applications ed W L Steffen and O T Denmead (Berlin: Springer)
2. Richard's L A 1931 Capillary conduction of liquids through porous mediums Physics 1 318-33
3. Philip J R 1957 The theory of infiltration. 1 Soil Sci. 83 345-57
4. Sposito G 1990 Lie group invariance of Richard's equation Fluids in Hierarchical Porous Medium ed J Cushman (New York: Academic) pp 327-47
5. Edwards M P 1994 Classical symmetry reductions of nonlinear diffusion-convection equations Phys. Lett. A 190 149-54
6. El-labany S K, Elhanbaly A M and Sabry R 2002 Group classification and symmetry reduction of variable coefficient non-linear diffusion-convection equation J. Phys. A: Math. Gen. 35 8055-63
7. Sophocleous C 1996 Potential symmetries of nonlinear diffusion convection equations J. Phys. A. Math. Gen. 29 6951-9
8. Gandarias Ml 1996 Potential symmetries of a porous medium equation J. Phys. A: Math. Gen. 29 5919-34
9. Bluman G W and Cole J D 1969 The general similarity solution of the heat equation J. Math. Mech. 18 1025-42
10. Gandarias Ml, Romero J L and Diaz T M 1999 Nonclassical symmetry reductions of a porous medium equation with convection J. Phys. A: Math. Gen. 32 1461-73
11. Clarkson P A and Mansfield E 1994 On a shallow water wave equation Nonlinearity 7 975-99
12. Champagne B, Hereman W and Winternitz P 1991 The computer calculation of Lie point symmetries of large systems of differential equations Comput. Phys. Commun. 66 319-40
13. Ibragimov N H 1996 Lie Group Analysis of Differential Equations vol 3 (Boca Raton, FL: CRC Press)
14. Hillel D 1998 Environmental Soil Physics (New York: Academic)
15. Miyazaki T 1993 Water Flow in Soils (New York: Marcel Dekker)