  This paper is devoted to the negative flows of the AKNS hierarchy. The main
result of this work is the functional representation of the extended AKNS
hierarchy, composed of both positive (classical) and negative flows. We derive
a finite set of functional equations, constructed by means of the Miwa's
shifts, which contains all equations of the hierarchy. Using the obtained
functional representation we convert the nonlocal equations of the negative
subhierarchy into local systems of higher order, derive the generating function
of the conservation laws and the N-dark-soliton solutions for the extended AKNS
hierarchy. As an additional result we obtain the functional representation of
the Landau-Lifshitz hierarchy.
