B\"acklund-Darboux Transformations and Discretizations of N=2\; a=-2 Supersymmetric KdV Equation
Abstract
The N=2 \;a=-2 supersymmetric KdV equation is studied. A Darboux transformation and the corresponding B\"acklund transformation are constructed for this equation. Also, a nonlinear superposition formula is worked out for the associated B\"acklund transformation. The B\"acklund transformation and the related nonlinear superposition formula are used to construct integrable super semi-discrete and full discrete systems. The continuum limits of these discrete systems are also considered.
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