Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations
Kiselev, Arthemy V. ; Wolf, Thomas
arXiv, 0511071 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-11-24
Classification:  Mathematical Physics,  Mathematics - Analysis of PDEs,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  35Q53,  37K05,  37K10,  37K35,  58A50,  81T40 
@article{0511071,
     author = {Kiselev, Arthemy V. and Wolf, Thomas},
     title = {Supersymmetric Representations and Integrable Fermionic Extensions of
  the Burgers and Boussinesq Equations},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511071}
}

Kiselev, Arthemy V.; Wolf, Thomas. Supersymmetric Representations and Integrable Fermionic Extensions of
  the Burgers and Boussinesq Equations. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511071/