Tau-functions and generalized integrable hierarchies (Q1311695)

The purpose of this work is to provide an explicit relation between the tau-functions and the variables of the zero-curvature formalism. It is found that there is not a one-to-one correspondence between the zero- curvature and the Kac-Wakimoto hierarchies: only a subset of both classes are related. The link between the two formalisms is provided by the ``dressing transformations''. It is also obtained an algorithm to find the variables of the zero- curvature hierarchies in terms of the tau-functions. The formalism also clarifies the connection between the zero-curvature hierarchies and the Hirota-type hierarchies of Kac and Wakimoto.