Super KP equations and Darboux transformations: another perspective on the Jacobian Super KP hierarchy

We generalize to the supersymmetric case the representation of the KP hierarchy as a set of conservation laws for the generating series of the conserved densities. We show that the hierarchy so obtained is isomorphic to the JSKP of Mulase and Rabin. We identify its “bosonic content” with the so-called Darboux–KP hierarchy, which geometrically encompasses the theory of Darboux–Bäcklund transformations, and is an extension both of the KP theory and of the modified KP theory. Finally, we show how the hierarchy can be linearized and how the supersymmetric counterpart of a wide class of rational solutions can be quite explicitly worked out.