  Taking the standard zero curvature approach we derive an infinite set of
integrable equations, which taken together form the negative Volterra
hierarchy. The resulting equations turn out to be nonlocal, which is usual for
the negative flows. However, in some cases the nonlocality can be eliminated.
Studying the combined action of both positive (classical) and negative Volterra
flows, i.e. considering the differential consequences of equations of the
extended Volterra hierarchy, we deduce local equations which seem to be
promising from the viewpoint of applications. The presented results give
answers to some questions related to the classification of integrable
differential-difference equations. We also obtain dark solitons of the negative
Volterra hierarchy using an elementary approach.
