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GROUP FOLIATION OF DIFFERENTIAL EQUATIONS USING MOVING FRAMES

Part of: Partial differential equations Classical differential geometry Pseudogroups, differentiable groupoids and general structures on manifolds Representations of solutions

Published online by Cambridge University Press:  26 October 2015

ROBERT THOMPSON  and
FRANCIS VALIQUETTE
ROBERT THOMPSON
Affiliation:
Department of Mathematics, Carleton College, Northfield, MN 55057, USA; [email protected]
FRANCIS VALIQUETTE
Affiliation:
Department of Mathematics, SUNY at New Paltz, New Paltz, NY 12561, USA

Abstract

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We incorporate the new theory of equivariant moving frames for Lie pseudogroups into Vessiot’s method of group foliation of differential equations. The automorphic system is replaced by a set of reconstruction equations on the pseudogroup jets. The result is a completely algorithmic and symbolic procedure for finding both invariant and noninvariant solutions of differential equations admitting a symmetry group.

MSC classification

Primary: 35B06: Symmetries, invariants, etc. 53A55: Differential invariants (local theory), geometric objects
Secondary: 35C05: Solutions in closed form 58H05: Pseudogroups and differentiable groupoids
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 3 , 2015 , e22
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2015

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