Tau-Functions and Generalized Integrable Hierarchies

Abstract

The tau-function formalism for a class of generalized ``zero-curvature'' integrable hierarchies of partial differential equations, is constructed. The class includes the Drinfel'd-Sokolov hierarchies. A direct relation between the variables of the zero-curvature formalism and the tau-functions is established. The formalism also clarifies the connection between the zero-curvature hierarchies and the Hirota-type hierarchies of Kac and Wakimoto.