Binary nonlinearization of the super AKNS system

TL;DR

This paper develops a binary nonlinearization method for the super AKNS spectral problem, leading to a super finite-dimensional integrable Hamiltonian system with explicit forms and integrals of motion.

Contribution

It introduces a novel binary nonlinearization approach for the super AKNS system and constructs an explicit super finite-dimensional integrable Hamiltonian system.

Findings

Established the binary nonlinearization of the super AKNS spectral problem.

Derived the super finite-dimensional integrable Hamiltonian system.

Provided explicit super Hamiltonian forms and integrals of motion.

Abstract

We establish the binary nonlinearization approach of the spectral problem of the super AKNS system, and then use it to obtain the super finite-dimensional integrable Hamiltonian system in supersymmetry manifold $\mathbb{R}^{4N|2N}$. The super Hamiltonian forms and integrals of motion are given explicitly.