The Hamiltonian structure of the N=2 supersymmetric GNLS hierarchy

TL;DR

This paper constructs Hamiltonian structures and recursion operators for the N=2 supersymmetric GNLS hierarchy, explores its bosonic limits, and uncovers a rich N=4 supersymmetry structure in specific cases.

Contribution

It introduces new local and nonlocal integrals and explicitly constructs Hamiltonian structures and symmetry transformations for the hierarchy.

Findings

Derived new local and nonlocal integrals for the hierarchy.

Constructed Hamiltonian structures and recursion operators in superfield form.

Uncovered N=4 supersymmetry in the n=1, m=1 case.

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.