Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations
We construct new integrable coupled systems of N = 1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are appl...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2006 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146439 |
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| Zitieren: | Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations / A.V. Kiselev, T. Wolf // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 27 назв. — англ. |
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Kiselev, A.V. Wolf, T. 2019-02-09T17:05:39Z 2019-02-09T17:05:39Z 2006 Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations / A.V. Kiselev, T. Wolf // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 27 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35Q53; 37K05; 37K10; 37K35; 58A50; 81T40 https://nasplib.isofts.kiev.ua/handle/123456789/146439 We construct new integrable coupled systems of N = 1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian structures. A fermionic extension of the Burgers equation is related with the Burgers flows on associative algebras. A Gardner's deformation is found for the bosonic super-field dispersionless Boussinesq equation, and unusual properties of a recursion operator for its Hamiltonian symmetries are described. Also, we construct a three-parametric supersymmetric system that incorporates the Boussinesq equation with dispersion and dissipation but never retracts to it for any values of the parameters. The authors thank V.V. Sokolov for formulation of the classification problem and also thank A.V. Mikhailov, A. Sergyeyev, and A.S. Sorin for helpful discussions. The authors are greatly indebted to the referees for their remarks and suggestions. T.W. wishes to thank W. Neun or discussions and the SHARCNET consortia for computer access. The research of A.K. was partially supported by the Scientific and Technological Research Council of Turkey (TUBITAK). A part of this research was carried out while A.K. was visiting at Brock University and at Middle East Technical University (Ankara). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations |
| spellingShingle |
Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations Kiselev, A.V. Wolf, T. |
| title_short |
Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations |
| title_full |
Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations |
| title_fullStr |
Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations |
| title_full_unstemmed |
Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations |
| title_sort |
supersymmetric representations and integrable fermionic extensions of the burgers and boussinesq equations |
| author |
Kiselev, A.V. Wolf, T. |
| author_facet |
Kiselev, A.V. Wolf, T. |
| publishDate |
2006 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We construct new integrable coupled systems of N = 1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian structures. A fermionic extension of the Burgers equation is related with the Burgers flows on associative algebras. A Gardner's deformation is found for the bosonic super-field dispersionless Boussinesq equation, and unusual properties of a recursion operator for its Hamiltonian symmetries are described. Also, we construct a three-parametric supersymmetric system that incorporates the Boussinesq equation with dispersion and dissipation but never retracts to it for any values of the parameters.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146439 |
| citation_txt |
Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations / A.V. Kiselev, T. Wolf // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 27 назв. — англ. |
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AT kiselevav supersymmetricrepresentationsandintegrablefermionicextensionsoftheburgersandboussinesqequations AT wolft supersymmetricrepresentationsandintegrablefermionicextensionsoftheburgersandboussinesqequations |
| first_indexed |
2025-11-28T11:05:32Z |
| last_indexed |
2025-11-28T11:05:32Z |
| _version_ |
1850853662196236288 |