The Hamiltonian structure of the N=2 supersymmetric GNLS hierarchy

Abstract

The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N=2 supersymmetric (n,m)-GNLS hierarchy are constructed in terms of N=2 superfields in two different superfield bases with local evolution equations. Their bosonic limits are studied in detail. New local and nonlocal bosonic and fermionic integrals both for the N=2 supersymmetric (n,m)-GNLS hierarchy and its bosonic counterparts are derived. As an example, in the n=1, m=1 case, the algebra and the symmetry transformations for some of them are worked out and a rich N=4 supersymmetry structure is uncovered.

12 pages, Latex

References in corpus (6)

• Toward the construction of N=2 supersymmetric integrable hierarchies
• New Integrable Extensions of N=2 KdV and Boussinesq Hierarchies
• Manifestly Supersymmetric Lax Integrable Hierarchies
• The Discrete Symmetries of the N=2 Supersymmetric GNLS Hierarchies
• The Discrete Symmetry of the N=2 Supersymmetric Modified NLS Hierarchy
• N=2 Superintegrable f-Toda Mapping and Super-NLS Hierarchy in the (1|2) Superspace

Cited by in corpus (6)

• N=2 local and N=4 nonlocal reductions of supersymmetric KP hierarchy in N=2 superspace
• The N=2 supersymmetric Toda lattice and matrix models
• A note on real forms of the complex N=4 supersymmetric Toda chain hierarchy in real N=2 and N=4 superspaces
• Coset approach to the N=2 supersymmetric matrix GNLS hierarchies
• Real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy in real N=1 and twisted N=2 superspaces
• N=2 supersymmetric unconstrained matrix GNLS hierarchies are consistent