On the equivalence of two super Korteweg\u2013deVries theories: A bi\u2010Hamiltonian viewpoint

From a bi-Hamiltonian viewpoint the equivalence of two supersymmetric Korteweg-deVries theories, introduced by Manin-Radul and Laberge-Mathieu, is discussed herein. It is shown that the transformation connecting the two theories (proposed recently in the literature) preserves the bi-Hamiltonian structures; moreover, another derivation of this transformation, stemming from bi-Hamiltonian reduction theory and strongly emphasizing the geometrical meaning of the above equivalence, is presented