On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces
The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of the symmetry properties of both the classical and supe...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147112 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces / S. Bertrand, A.M. Grundland, A.J. Hariton // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862732080586162176 |
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| author | Bertrand, S. Grundland, A.M. Hariton, A.J. |
| author_facet | Bertrand, S. Grundland, A.M. Hariton, A.J. |
| citation_txt | On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces / S. Bertrand, A.M. Grundland, A.J. Hariton // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of the symmetry properties of both the classical and supersymmetric versions of the Gauss-Weingarten equations is performed. A supersymmetric generalization of the conjecture establishing the necessary conditions for a system to be integrable in the sense of soliton theory is formulated and illustrated by the examples of supersymmetric versions of the sine-Gordon equation and the Gauss-Codazzi equations.
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| first_indexed | 2025-12-07T19:30:05Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147112 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:30:05Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bertrand, S. Grundland, A.M. Hariton, A.J. 2019-02-13T16:52:14Z 2019-02-13T16:52:14Z 2015 On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces / S. Bertrand, A.M. Grundland, A.J. Hariton // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q51; 53A05; 22E70 DOI:10.3842/SIGMA.2015.046 https://nasplib.isofts.kiev.ua/handle/123456789/147112 The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of the symmetry properties of both the classical and supersymmetric versions of the Gauss-Weingarten equations is performed. A supersymmetric generalization of the conjecture establishing the necessary conditions for a system to be integrable in the sense of soliton theory is formulated and illustrated by the examples of supersymmetric versions of the sine-Gordon equation and the Gauss-Codazzi equations. This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of
 Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html.
 We thank professor D. Levi (University of Roma Tre) for useful discussions on this topic. AMG’s
 work was supported by a research grant from NSERC. SB acknowledges a doctoral fellowship
 provided by the FQRNT of the Gouvernement du Qu´ebec. AJH wishes to acknowledge and
 thank the Mathematical Physics Laboratory of the Centre de Recherches Math´ematiques for
 the opportunity to contribute to this research. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces Article published earlier |
| spellingShingle | On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces Bertrand, S. Grundland, A.M. Hariton, A.J. |
| title | On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces |
| title_full | On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces |
| title_fullStr | On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces |
| title_full_unstemmed | On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces |
| title_short | On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces |
| title_sort | on the integrability of supersymmetric versions of the structural equations for conformally parametrized surfaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147112 |
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