  In this paper we study the inter-relationship between the integrable KP
hierarchy, nonlinear $\hat{W}_{\infty}$ algebra and conformal noncompact
$SL(2,R)/U(1)$ coset model at the classical level. We first derive explicitly
the Possion brackets of the second Hamiltonian structure of the KP hierarchy,
then use it to define the $\hat{W}_{1+\infty}$ algebra and its reduction
$\hat{W}_{\infty}$. Then we show that the latter is realized in the
$SL(2,R)/U(1)$ coset model as a hidden current algebra, through a free field
realization of $\hat{W}_{\infty}$, in closed form for all higher-spin currents,
in terms of two bosons. An immediate consequence is the existence of an
infinite number of KP flows in the coset model, which preserve the
$\hat{W}_{\infty}$ current algebra.
