Zero curvature formalism in superspace

We discuss the generalization of the Drinfeld-Sokolov formalism to superspace in the case of supersymmetric integrable systems. We bring out the connection between this and the zero curvature formulations, for these systems, in components. Various examples are worked out in detail. We show how the symmetric space techniques can be profitably used to solve the zero curvature conditions and to obtain the hierarchy of equations in the case of sAKNS hierarchy. The dynamical equations are formulated also as the Cartan-Maurer equations in superspace and we show how the zero curvature condition can be solved, alternately, by expanding potentials according to the grading charge. We also discuss the sTB-B hierarchy to bring out some open questions.