Existence and Construction of Vessiot Connections
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 s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2009-09-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.092 |
| _version_ | 1818482580952973312 |
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| author | Dirk Fesser Werner M. Seiler |
| author_facet | Dirk Fesser Werner M. Seiler |
| author_sort | Dirk Fesser |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T11:49:11Z |
| format | Article |
| id | doaj.art-029777bbefac4367a1804b434414ed9c |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-10T11:49:11Z |
| publishDate | 2009-09-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-029777bbefac4367a1804b434414ed9c2022-12-22T01:49:58ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-09-015092Existence and Construction of Vessiot ConnectionsDirk FesserWerner M. SeilerA 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.http://dx.doi.org/10.3842/SIGMA.2009.092formal integrabilityintegral elementinvolutionpartial differential equationVessiot connectionVessiot distribution |
| spellingShingle | Dirk Fesser Werner M. Seiler Existence and Construction of Vessiot Connections Symmetry, Integrability and Geometry: Methods and Applications formal integrability integral element involution partial differential equation Vessiot connection Vessiot distribution |
| title | Existence and Construction of Vessiot Connections |
| title_full | Existence and Construction of Vessiot Connections |
| title_fullStr | Existence and Construction of Vessiot Connections |
| title_full_unstemmed | Existence and Construction of Vessiot Connections |
| title_short | Existence and Construction of Vessiot Connections |
| title_sort | existence and construction of vessiot connections |
| topic | formal integrability integral element involution partial differential equation Vessiot connection Vessiot distribution |
| url | http://dx.doi.org/10.3842/SIGMA.2009.092 |
| work_keys_str_mv | AT dirkfesser existenceandconstructionofvessiotconnections AT wernermseiler existenceandconstructionofvessiotconnections |