Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation

For a generalized super KdV equation, three Darboux transformations and the corresponding Backlund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations. The reduction of one of the Backlund{Darboux transformations and the corresponding discrete system are considered for Kupershmidt's super KdV equation. When all the odd variables vanish, a nonlinear superposition formula is obtained for Levi's Backlund transformation for the KdV equation.