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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 092, 41 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.092 (Mi sigma438) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Existence and Construction of Vessiot Connections

Dirk Fessera, Werner M. Seilerb

a IWR, Universität Heidelberg, INF 368, 69120 Heidelberg, Germany
b AG "Computational Mathematics", Universität Kassel, 34132 Kassel, Germany
Full-text PDF (533 kB) Citations (8)
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DOI: https://doi.org/10.3842/SIGMA.2009.092
Abstract: A rigorous formulation of Vessiot's vector field approach to the analysis of general systems of partial differential equations is provided. It is shown that this approach is equivalent to the formal theory of differential equations and that it can be carried through if, and only if, the given system is involutive. As a by-product, we provide a novel characterisation of transversal integral elements via the contact map.
Keywords: formal integrability; integral element; involution; partial differential equation; Vessiot connection; Vessiot distribution.
Received: May 5, 2009; in final form September 14, 2009; Published online September 25, 2009
Bibliographic databases:
Document Type: Article
MSC: 35A07; 35A30; 35N99; 58A20
Language: English
Citation: Dirk Fesser, Werner M. Seiler, “Existence and Construction of Vessiot Connections”, SIGMA, 5 (2009), 092, 41 pp.
Citation in format AMSBIB
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