A fully supersymmetric AKNS theory

We construct a fully supersymmetric biHamiltonian theory in four superfields, admitting zero curvature and Lax formulation. This theory is an extension of the classical AKNS, which can be recovered as a reduction. Other supersymmetric theories are obtained as reductions of the susy AKNS, namely a nonlinear Schrödinger, a modified KdV and the Manin-Radul KdV. The susy nonlinear Schrödinger hierarchy is related to the one of Roelofs and Kersten; we determine its biHamiltonian and Lax formulation. Finally, we show that the susy KdV's mentioned before are related through a susy Miura map.