Abstract
For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the Bäcklund transformation found earlier by Liu and Xie (2004 Phys. Lett. A 325 139–43). The Darboux transformation and the related Bäcklund transformation are used to construct integrable super differential–difference and difference–difference systems. The continuum limits of these discrete systems and of their Lax pairs are also considered.
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