# Nonlinear integrable couplings of a generalized super Ablowitz-Kaup-Newell-Segur hierarchy and its super bi-Hamiltonian structures

## TL;DR

This paper introduces a new generalized matrix spectral problem related to the AKNS hierarchy, establishes its super soliton hierarchy, and derives super bi-Hamiltonian structures using super variational identities.

## Contribution

It presents a novel generalized $5\times5$ matrix spectral problem linked to an enlarged Lie super algebra and constructs its super soliton hierarchy with Hamiltonian structures.

## Key findings

- Proposes a new generalized spectral problem of AKNS type.
- Establishes the super soliton hierarchy associated with the problem.
- Derives super bi-Hamiltonian structures using super variational identities.

## Abstract

In this paper, a new generalized $5\times5$ matrix spectral problem of Ablowitz-Kaup-Newell-Segur(AKNS) type associated with the enlarged matrix Lie super algebra is proposed and its corresponding super soliton hierarchy is established. The super variational identities is used to furnish super-Hamiltonian structures for the resulting super soliton hierarchy.