Super KP equations and Darboux transformations: another perspective on theJacobian Super KP hierarchy

We generalize to the supersymmetric case the representation of the KP hiera rchy as a set of conservation laws for the generating series of the conserv ed densities. We show that the hierarchy so obtained is isomorphic to the J SKP of Mulase and Rabin. We identify its "bosonic content" with the so-call ed Darboux-KP hierarchy, which geometrically encompasses the theory of Darb oux-Backlund transformations, and is an extension both of the KP theory and of the modified KP theory. Finally, we show how the hierarchy can be linea rized and how the supersymmetric counterpart of a wide class of rational so lutions can be quite explicitly worked out. (C) 2000 Elsevier Science B.V. All rights reserved.