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 semi-discrete and fully discrete systems are presented. Also, the continuum limits of the relevant discrete systems are worked out.
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