Bi-Hamiltonian structure of the N=2 supersymmetric α=1 KdV hierarchy

Abstract

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 supersymmetric α = 1 KdV hierarchy possesses two different subalgebras of N = 2 supersymmetry.

Supersymmetry and the KdV equations for integrable hierarchies with a half-integer gradation

“…Soon after, Mathieu and Labelle wrote down the equations for the N = 2 supersymmetric KdV equations [7] (see also [8]). Kersten and Sorin studied the bihamiltonian structure of N = 2 supersymmetric KdV model within the superfield formalism [9]. Das and Galvão have derived the supersymmetric KdV equation from the self-duality conditions imposed on four-dimensional Yang-Mills potential [10].…”

N = 2 supersymmetric a=4-Korteweg–de Vries hierarchy derived via Gardner’s deformation of Kaup–Boussinesq equation

“…3,4,21 Moreover, system ͑3͒ with a = 4 is radically different from the other two, both from the Hamiltonian and Lax viewpoints. =d/ dx, which is obtained from P 2 a=4 by the shift u ‫ۋ‬ u + of the superfield u, see Refs.…”

N = 2 Supercomplexification of the Korteweg-de Vries, Sawada-Kotera and Kaup-Kupershmidt Equations

“…On the other hand, applications of the supersymmetry (SUSY) to the soliton theory provide a possibility of generalization of the integrable systems. The supersymmetric integrable equations [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] have drawn a lot of attention for a variety of reasons. In order to create a supersymmetric theory, we have to add to a system of k bosonic equations kN fermionic and k(N −1) bosonic fields (k = 1, 2 .…”