Supersymmetric KdV equation: Darboux transformation and discrete systems

For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the Backlund transformation found earlier by Liu and Xie (2004 Phys. Lett. A 325 139–43). The Darboux transformation and the related Backlund 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.