The KdV and modified KdV integrable hierarchies are shown to be different descriptions of the same 2D gravitational system - open-dosed string theory. Non-perturbative solutions of the multicritical unitary matrix models map to non-singular solutions of the 'renormalization group' equation for the string susceptibility, [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 [P, Q] = Q.