  In this paper we prove that the generating series of the Hodge integrals over
the moduli space of stable curves is a solution of a certain deformation of the
KdV hierarchy. This hierarchy is constructed in the framework of the
Dubrovin-Zhang theory of the hierarchies of the topological type. It occurs
that our deformation of the KdV hierarchy is closely related to the hierarchy
of the Intermediate Long Wave equation.
