Moving coframes and symmetries of differential equations

Morozov, Oleg I.

doi:10.1088/0305-4470/35/12/317

Cited by 32 publications

(33 citation statements)

References 6 publications

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“…Let ι : R → J 2 (E) be the inclusion map. Then we can find the Maurer-Cartan forms for the pseudo-group Sym(R) of contact symmetries of R from the restrictions θ 0 = ι * Θ 0 , θ i = ι * Θ i , ξ i = ι * Ξ i , σ ij = ι * Σ ij by standard procedures of Cartan's equivalence method, see [12,33,34] for details. Example 4.…”

Section: The Moving Coframe Methodsmentioning

confidence: 99%

Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches

Morozov¹

2005

SIGMA

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Section: The Moving Coframe Methodsmentioning

confidence: 99%

Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches

Morozov¹

2005

SIGMA

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“…In this section, we outline the algorithm of computing Maurer-Cartan forms for pseudogroups of contact symmetries for DEs of the second order with one dependent variable, see details in [32,35,36]. All considerations are of local nature, and all mappings are real analytic.…”

Section: Cartan's Structure Theory Of Symmetry Pseudo-groups Of Desmentioning

confidence: 99%

Coverings of Differential Equations and Cartan’s Structure Theory of Lie Pseudo-Groups

Morozov

2007

Acta Appl Math

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“…Applications have included complete classifications of differential invariants and their syzygies, equivalence and symmetry properties of submanifolds, rigidity theorems, invariant signatures in computer vision, [3,7,9,57], joint invariants and joint differential invariants, [8,57], invariant numerical algorithms, [57,58], classical invariant theory, [4,56], Poisson geometry and solitons, [49], and the calculus of variations, [37,38]. New applications of these methods to computation of symmetry groups and classification of partial differential equations can be found in [48,52].…”

Section: Introductionmentioning

confidence: 99%

Maurer–Cartan forms and the structure of Lie pseudo-groups

Olver

Pohjanpelto

2005

Sel. math., New ser.

124

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Sur la théorie, si importante sans doute, mais pour nous si obscure, des ≪groupes de Lie infinis≫, nous ne savons rien que ce qui se trouve dans les mémoires de Cartan, premiere explorationà travers une jungle presque impénétrable; mais cell-ci menace de se refermer sur les sentiers déjà tracés, si l'on ne procède bientôtà un indispensable travail de défrichement.-André Weil, [76] Abstract.This paper begins a series devoted to developing a general and practical theory of moving frames for infinite-dimensional Lie pseudo-groups. In this first, preparatory part, we present a new, direct approach to the construction of invariant Maurer-Cartan forms and the Cartan structure equations for a pseudo-group. Our approach is completely explicit and avoids reliance on the theory of exterior differential systems and prolongation.The second paper [60] will apply these constructions in order to develop the moving frame algorithm for the action of the pseudo-group on submanifolds. The third paper [61] will apply Gröbner basis methods to prove a fundamental theorem on the freeness of pseudo-group actions on jet bundles, and a constructive version of the finiteness theorem of Tresse and Kumpera for generating systems of differential invariants and also their syzygies. Applications of the moving frame method include practical algorithms for constructing complete systems of differential invariants and invariant differential forms, classifying their syzygies and recurrence relations, analyzing invariant variational principles, and solving equivalence and symmetry problems arising in geometry and physics.

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Moving coframes and symmetries of differential equations

Cited by 32 publications

References 6 publications

Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches

Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches

Coverings of Differential Equations and Cartan’s Structure Theory of Lie Pseudo-Groups

Maurer–Cartan forms and the structure of Lie pseudo-groups

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