Abstract
The construction of Miura and Bäcklund transformations for A n mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in the well known sl(2) case, we derive and relate the equations of motion for the two hierarchies. Moreover, the Miura-gauge transformation is not unique, instead, it is shown to be connected to a set of generators labeled by the exponents of A n . The construction of generalized gauge-Bäcklund transformation for the A n -KdV hierarchy is obtained as a composition of Miura and Bäcklund-gauge transformations for A n -mKdV hierarchy. The zero curvature representation provide a framework which is universal within all flows and generate systematically Bäcklund transformations for the entirely hierarchy.
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