GROUP FOLIATION OF DIFFERENTIAL EQUATIONS USING MOVING FRAMES

Abstract

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.

Keywords

• 35B06
• 53A55 (primary)
• 35C05
• 58H05 (secondary)