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A comparison of four approaches to the calculation of conservation laws

Published online by Cambridge University Press:  16 April 2002

THOMAS WOLF
THOMAS WOLF
Affiliation:
Department of Mathematics, Brock University, St. Catharines, ON L2S 3A1, Canada
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Abstract

The paper compares computational aspects of four approaches to compute conservation laws of single Differential Equations (DEs) or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer algebra programs, is that each DE has to be solvable for a leading derivative. Extra constraints for the conservation laws can be specified. Examples include new conservation laws that are non-polynomial in the functions, that have an explicit variable dependence and families of conservation laws involving arbitrary functions. The following equations are investigated in examples: Ito, Liouville, Burgers, Kadomtsev–Petviashvili, Karney–Sen–Chu–Verheest, Boussinesq, Tzetzeica, Benney.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 2 , April 2002 , pp. 129 - 152
Copyright
2002 Cambridge University Press

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