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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2006-02-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2006/Paper030/ |
| _version_ | 1819292260349509632 |
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| author | Arthemy V. Kiselev Thomas Wolf |
| author_facet | Arthemy V. Kiselev Thomas Wolf |
| author_sort | Arthemy V. Kiselev |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-24T03:51:42Z |
| format | Article |
| id | doaj.art-6bad317919b64979addf1547b1f7690d |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-24T03:51:42Z |
| publishDate | 2006-02-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-6bad317919b64979addf1547b1f7690d2022-12-21T17:16:33ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592006-02-012030Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq EquationsArthemy V. KiselevThomas WolfWe 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.http://www.emis.de/journals/SIGMA/2006/Paper030/integrable super-equationsfermionic extensionsBurgers equationBoussinesq equation |
| spellingShingle | Arthemy V. Kiselev Thomas Wolf Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations Symmetry, Integrability and Geometry: Methods and Applications integrable super-equations fermionic extensions Burgers equation Boussinesq equation |
| title | 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_short | 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 |
| topic | integrable super-equations fermionic extensions Burgers equation Boussinesq equation |
| url | http://www.emis.de/journals/SIGMA/2006/Paper030/ |
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