Bäcklund-Darboux Transformations and Discretizations of $N=2a=-2$ Supersymmetric KdV Equation

Abstract

The $N=2a=-2$ supersymmetric KdV equation is studied. A Darboux transformation and the corresponding Bäcklund transformation are constructed for this equation. Also, a nonlinear superposition formula is worked out for the associated Bäcklund transformation. The Bäcklund 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.

arXiv comment12 pages

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Cited by in corpus (1)

• On the $3D$ consistency of a Grassmann extended lattice Boussinesq system