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Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations
Arthemy V. Kiselevab, Thomas Wolfc a Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
b Department of Higher Mathematics, Ivanovo State Power University, 34 Rabfakovskaya Str., Ivanovo, 153003 Russia
c Department of Mathematics, Brock University, 500 Glenridge Ave., St. Catharines, Ontario, Canada L2S 3A1
Аннотация:
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.
Ключевые слова:
integrable super-equations; fermionic extensions;Burgers equation; Boussinesq equation.
Поступила: 26 ноября 2005 г.; в окончательном варианте 25 февраля 2006 г.; опубликована 28 февраля 2006 г.
Образец цитирования:
Arthemy V. Kiselev, Thomas Wolf, “Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations”, SIGMA, 2 (2006), 030, 19 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma58 https://www.mathnet.ru/rus/sigma/v2/p30
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