  Recently R. Pandharipande, J. Solomon and R. Tessler initiated a study of the
intersection theory on the moduli space of Riemann surfaces with boundary. They
conjectured that the generating series of the intersection numbers is a
specific solution of a system of PDEs, that they called the open KdV equations.
In this paper we show that the open KdV equations are closely related to the
equations for the wave function of the KdV hierarchy. This allows us to give an
explicit formula for the specific solution in terms of Witten's generating
series of the intersection numbers on the moduli space of stable curves.
