  The KdV and modified KdV integrable hierarchies are shown to be different
descriptions of the same 2D gravitational system -- open-closed string theory.
Non-perturbative solutions of the multi-critical unitary matrix models map to
non-singular solutions of the `renormalisation group' equation for the string
susceptibility, $[\tilde{P},Q]=Q$. We also demonstrate that the large N
solutions of unitary matrix integrals in external fields, studied by Gross and
Newman, equal the non-singular pure closed-string solutions of
$[\tilde{P},Q]=Q$.
