A supersymmetric AKNS problem and its Darboux-B\"acklund transformations and discrete systems

TL;DR

This paper develops Darboux-Bäcklund transformations for a supersymmetric AKNS problem, enabling the construction of integrable discrete super systems and their continuum limits, advancing the understanding of supersymmetric integrable models.

Contribution

It introduces new Darboux and Bäcklund transformations for supersymmetric integrable equations and constructs associated discrete super systems, including semi-discrete and fully discrete models.

Findings

Constructed elementary and binary Darboux transformations for supersymmetric AKNS.

Derived Darboux and Bäcklund transformations for supersymmetric modified KdV, sinh-Gordon, and NLS equations.

Presented integrable discrete super systems and their continuum limits.

Abstract

In this paper, we consider a supersymmetric AKNS spectral problem. Two elementary and a binary Darboux transformations are constructed. By means of reductions, Darboux and B\"acklund transformations are given for the supersymmetric modified Korteweg-de Vries, sinh-Gordon and nonlinear Schr\"odinger equations. These Darboux and B\"acklund transformations are adopted for the constructions of integrable discrete super systems, and both semi-discrete and fully discrete systems are presented. Also, the continuum limits of the relevant discrete systems are worked out.