  In this paper, we establish Liouville correspondences for the integrable
two-component Camassa-Holm hierarchy, the two-component Novikov (Geng-Xue)
hierarchy, and the two-component dual dispersive water wave hierarchy by means
of the related Liouville transformations. This extends previous results on the
scalar Camassa-Holm and KdV hierarchies, and the Novikov and Sawada-Kotera
hierarchies to the multi-component case.
