Bi - Hamiltonian structure of the N = 2 supersymmetric α = 1 KdV hierarchy
نویسندگان
چکیده
The N = 2 supersymmetric α = 1 KdV hierarchy in N = 2 superspace is considered and its rich symmetry structure is uncovered. New nonpolynomial and nonlocal, bosonic and fermionic symmetries and Hamiltonians, bi-Hamiltonian structure as well as a recursion operator connecting all symmetries and Hamiltonian structures of the N = 2 α = 1 KdV hierarchy are constructed in explicit form. It is observed that the algebra of symmetries of the N = 2 super-symmetric α = 1 KdV hierarchy possesses two different subalgebras of N = 2 supersymmetry.
منابع مشابه
Bi-hamiltonian Structure of the N = 2 Supersymmetric Α = 1 Kdv Hierarchy Bi-hamiltonian Structure of the N=2 Supersymmetric Α = 1 Kdv Hierarchy
The N = 2 supersymmetric α = 1 KdV hierarchy in N = 2 superspace is considered and its rich symmetry structure is uncovered. New nonpolynomial and nonlocal, bosonic and fermionic symmetries and Hamiltonians, bi-Hamiltonian structure as well as a recursion operator connecting all symmetries and Hamiltonian structures of the N = 2 α = 1 KdV hierarchy are constructed in explicit form. It is observ...
متن کامل2 Deformation and Recursion for the N = 2 α = 1 Supersymmetric KdV - hierarchy
A detailed description is given for the construction of the deformation of the N = 2 supersymmetric α = 1 KdV-equation, leading to the recursion operator for symmetries and the zero-th Hamiltonian structure; the solution to a longstanding problem.
متن کاملBi - Hamiltonian Structure of the Supersymmetric Nonlinear Schrödinger Equation
We show that the supersymmetric nonlinear Schrödinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric two boson hierarchy through a field redefinition. We also show how the two Hamiltonian structures of the supersymmetric KdV equation can be derived from a Hamiltonian reduction of the supersymmetric two b...
متن کاملA Note on the Third Family of N = 2 Supersymmetric KdV
We propose a hamiltonian formulation of the N = 2 supersymmetric KP type hierarchy recently studied by Krivonos and Sorin. We obtain a quadratic hamiltonian structure which allows for several reductions of the KP type hierarchy. In particular , the third family of N = 2 KdV hierarchies is recovered. We also give an easy construction of Wronskian solutions of the KP and KdV type equations.
متن کاملThe Bi-Hamiltonian Structure of the Perturbation Equations of KdV Hierarchy
The bi-Hamiltonian structure is established for the perturbation equations of KdV hierarchy and thus the perturbation equations themselves provide also examples among typical soliton equations. Besides, a more general bi-Hamiltonian integrable hierarchy is proposed and a remark is given for a generalization of the resulting perturbation equations to 1 + 2 dimensions. Perturbation theory is the ...
متن کامل