A Supersymmetric AKNS Problem and Its Darboux‐Bäcklund Transformations and Discrete Systems

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 Bäcklund transformations are given for the supersymmetric modified Korteweg‐de Vries, sinh‐Gordon, and nonlinear Schrödinger equations. These Darboux and Bäcklund transformations are adopted for the constructions of integrable discrete super systems, and both semidiscrete and fully discrete systems are presented. Also, the continuum limits of the relevant discrete systems are worked out.