900 research outputs found
Odd Bihamiltonian Structure of New Supersymmetric N=2,4 KdV And Odd SUSY Virasoro - Like Algebra
The general method of the supersymmetrization of the soliton equations with
the odd (bi) hamiltonian structure is established. New version of the
supersymmetric N=2,4 (Modified) Korteweg de Vries equation is given, as an
example. The second odd Hamiltonian operator of the SUSY KdV equation generates
the odd N=2,4 SUSY Virasoro - like algebra.Comment: 13 pages LaTe
Extensions of the N=2 Supersymmetric a=-2 Boussinesq Hierarchy
We present two different Lax operators for a manifestly N=2 supersymmetric
extension of "a=-2" Boussinesq hierarchy . The first is the supersymmetric
generalization of the Lax operator of the Modified KdV equation. The second is
the generalization of the supersymmetric Lax operator of the N=2 supersymmetric
a=-2 KdV system. The gauge transformation of the first Lax operator provide the
Miura link between the "small" N=4 supersymmetric conformal algebra and the
supersymmetric algebra .Comment: LaTex, new references added, minor typos corrected, e-mail:
[email protected]
A 2 - Component or N=2 Supersymmetric Camassa - Holm Equation
The extended N=2 supersymmetric Camasa - Holm equation is presented. It is
accomplishe by formulation the supersymmeytric version of the Fuchssteiner
method. In this framework we use two supersymmetric recursion operators of the
N=2, Korteweg - de Vries equation and constructed two different
version of the supersymmetric Camassa - Holm equation. The bosonic sector of
N=2, supersymmetric Camassa - Holm equation contains two component
generalization of this equation considered by Chen, Liu and Zhang and as a
special case two component generalized Hunter - Saxton equation considered by
Aratyn, Gomes and Zimerman, As a byproduct of our analysis we defined the N=2
supersymmetric Hunter - Saxton equation. The bihamiltonian structure is
constructed for the supersymmetric N=2, Camassa - Holm equation.Comment: 9 pages, Latex,corrected typo
The Integrability of New Two-Component KdV Equation
We consider the bi-Hamiltonian representation of the two-component coupled
KdV equations discovered by Drinfel'd and Sokolov and rediscovered by Sakovich
and Foursov. Connection of this equation with the supersymmetric
Kadomtsev-Petviashvilli-Radul-Manin hierarchy is presented. For this new
supersymmetric equation the Lax representation and odd Hamiltonian structure is
given
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