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The $N=2 \;a=-2$ supersymmetric KdV equation is studied. A Darbouxtransformation and the corresponding B\"acklund transformation are constructedfor this equation. Also, a nonlinear superposition formula is worked out forthe associated B\"acklund transformation. The B\"{a}cklund transformation andthe related nonlinear superposition formula are used to construct integrablesuper semi-discrete and full discrete systems. The continuum limits of thesediscrete systems are also considered.

B\"acklund-Darboux Transformations and Discretizations of $N=2\; a=-2$ Supersymmetric KdV Equation