  We provide a description of the Drinfeld-Sokolov Hamiltonian reduction for
the construction of classical W-algebras within the framework of Poisson vertex
algebras. In this context, the gauge group action on the phase space is
translated in terms of (the exponential of) a Lie conformal algebra action on
the space of functions. Following the ideas of Drinfeld and Sokolov, we then
establish under certain sufficient conditions the applicability of the
Lenard-Magri scheme of integrability and the existence of the corresponding
integrable hierarchy of bi-Hamiltonian equations.
