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MiS Preprint
51/2007

Symmetry approaches for reductions of PDEs, differential constraints and Lagrange-Charpit method.

Boris Kruglikov

Abstract

Many methods for reduction and simplification of partial differential equations are known. They provide various generalizations of the original symmetry approach of Sophus Lie. Plenty of relations between these methods have been explored in the literature.

In this short paper a unifying approach will be discussed. It is rather close to the method of differential constraints, but we make the latter rigorous basing on recent advances in compatibility theory of non-linear overdetermined systems and algebro-geometric methods for PDEs.

Received:
May 25, 2007
Published:
May 25, 2007
MSC Codes:
34A05, 35N10, 58A20
Keywords:
compatibility, differential constraint, symmetry, reduction, multi-bracket

Related publications

inJournal
2008 Repository Open Access
Boris Kruglikov

Symmetry approaches for reductions of PDEs, differential constraints, and Lagrange-Charpit method

In: Acta applicandae mathematicae, 101 (2008) 1/3, pp. 145-161