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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2006 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146439 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146439 |
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dspace |
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irk-123456789-1464392019-02-10T01:23:29Z Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations Kiselev, A.V. Wolf, T. 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. 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146439 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Kiselev, A.V. Wolf, T. |
| spellingShingle |
Kiselev, A.V. Wolf, T. Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kiselev, A.V. Wolf, T. |
| author_sort |
Kiselev, A.V. |
| title |
Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:24:23Z |
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2023-05-20T17:24:23Z |
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