Binary Nonlinearization of the Super Akns System Under an Implicit Symmetry Constraint

TL;DR

This paper introduces an implicit symmetry constraint for the super AKNS system, decomposes it into finite-dimensional super Hamiltonian systems, and demonstrates their integrability within a supersymmetry framework.

Contribution

It presents a novel implicit symmetry constraint and a nonlinearization approach that decomposes the super AKNS system into integrable super Hamiltonian systems.

Findings

Super AKNS system is decomposed into two compatible finite-dimensional super systems.

The resulting super systems are shown to be integrable super Hamiltonian systems.

The systems are formulated within a supersymmetry manifold.

Abstract

For the super AKNS system, an implicit symmetry constraint between the potentials and the eigenfunctions is proposed. After introducing some new variables to explicitly express potentials, the super AKNS system is decomposed into two compatible finite-dimensional super systems (x-part and $t_n$-part). Furthermore, we show that the obtained super systems are integrable super Hamiltonian systems in supersymmetry manifold $\mathbb{R}^{4N+2|2N+2}$.