  In this article we study St\"{a}ckel representations of stationary KdV
systems. Using Lax formalism we prove that these systems have two different
representations as separable St\"{a}ckel systems of Benenti type, related with
different foliations of the stationary manifold. We do it by constructing an
explicit transformation between the jet coordinates of stationary KdV systems
and separation variables of the corresponding Benenti systems for arbitrary
number of degrees of freedom. Moreover, on the stationary manifold, we present
the explicit form of Miura map between both representations of stationary KdV
systems, which also yields their bi-Hamiltonian formulation.
