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 $W_{3}$ 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, $\alpha=-2,4$ Korteweg - de Vries equation and constructed two different version of the supersymmetric Camassa - Holm equation. The bosonic sector of N=2, $\alpha=4$ 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, $\alpha=4$ 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

Double Extended Cubic Peakon Equation

The Hamiltonian structure for the supersymmetric $N=2$ Novikov equation is presented. The bosonic sector give us two-component generalization of the cubic peakon equation. The double extended: two-component and two-peakon Novikov equation is defined. The Bi-Hamiltonian structure for this extended system is constructed.Comment: the misprints are correcte