Abstract
A super extension of the Korteweg-de Vries (KdV) equation proposed by Kupershmidt is studied. Its Bäcklund transformation is explicitly presented and a Lax pair is derived, so the integrability of this system is confirmed. The corresponding nonlinear superposition formula is constructed from the Bäcklund transformation and is interpreted as a fully discrete system, whose integrability is demonstrated by verifying its consistency around the cube (CAC) property and supplying a zero-curvature representation.
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