N=2 Superintegrable f-Toda Mapping and Super-NLS Hierarchy in the (1|2) Superspace

TL;DR

This paper introduces a new N=2 supersymmetric f-Toda mapping in (1|2) superspace, establishing its role as a symmetry of the N=2 super-NLS hierarchy and explicitly constructing its Hamiltonian structures and recursion operator.

Contribution

It presents the first N=2 supersymmetric f-Toda mapping in (1|2) superspace and derives its Hamiltonian structures and recursion operator using invariance conditions.

Findings

Constructed the first two Hamiltonian structures.

Derived the recursion operator for the hierarchy.

Identified a new representation for Hamiltonians.

Abstract

A new integrable N=2 supersymmetric f-Toda mapping in (1|2) superspace, acting like the symmetry transformation of N=2 supersymmetric NLS hierarchy, is proposed. The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N=2 super-NLS hierarchy are constructed in explicit form using only invariance conditions with respect to the f-Toda mapping. A new representation for its Hamiltonians is observed.