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Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations
Інший ID:
2000 Mathematics Subject Classification: 35Q53; 37K05; 37K10; 37K35; 58A50; 81T40
Посилання:
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.
Підтримка:
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).
Дата:
2006
Переглядів:
516
Завантажень:
231
Анотація:
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.
