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Computer algebra application for determining Lie and Lie-Bäcklund symmetries of differential equations. (English) Zbl 0691.35004

Summary: The application of computer algebra for determining Lie and Lie- Bäcklund (LB) symmetries of differential equations is considered. Algorithms for calculating the symmetries are developed and implemented on the basis of computer algebra systems. REDUCE, AMP and FORMAC. The most effective and advanced program is written in FORMAC. It finds LB symmetries completely automatically. In many cases the program yields the full algebra of symmetries. If the program fails in full integration of the determining system, it reduces the remaining determining equations to the system in involution.

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
68W30 Symbolic computation and algebraic computation
58J72 Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds

Software:

FORMAC; REDUCE; SPDE; LIE; LIE0
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Full Text: DOI

References:

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