Computer Algebra and Differential Equations

1994 ◽  
Keyword(s):  
Differential Equations ◽  
Computer Algebra

scholarly journals A comparison of four approaches to the calculation of conservation laws

2002 ◽  
Vol 13 (2) ◽  
pp. 129-152 ◽  
Author(s):  
THOMAS WOLF
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Computer Algebra ◽  
Computational Aspects

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.

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