An integrable generalization of the super Kaup-Newell soliton hierarchy and its bi-Hamiltonian structure

TL;DR

This paper introduces a new integrable super Kaup-Newell hierarchy, generalizes its structure, and demonstrates its bi-Hamiltonian formulation, expanding the mathematical framework of super integrable systems.

Contribution

It presents a novel integrable generalization of the super Kaup-Newell hierarchy and establishes its bi-Hamiltonian structure using Lie super-algebra techniques.

Findings

The generalized super KN hierarchy is integrable and bi-Hamiltonian.

A super soliton hierarchy with self-consistent sources is constructed.

The hierarchy is based on a Lie super-algebra B(0,1).

Abstract

An integrable generalization of the super Kaup-Newell(KN) isospectral problem is introduced and its corresponding generalized super KN soliton hierarchy are established based on a Lie super-algebra B(0,1) and super-trace identity in this paper. And the resulting super soliton hierarchy can be put into a super bi-Hamiltonian form. In addition, a generalized super KN soliton hierarchy with self-consistent sources is also presented.