  We consider initial-boundary value problems for the KdV equation $u_t + u_x +
6uu_x + u_{xxx} = 0$ on the half-line $x \geq 0$. For a well-posed problem, the
initial data $u(x,0)$ as well as one of the three boundary values $\{u(0,t),
u_x(0,t), u_{xx}(0,t)\}$ can be prescribed; the other two boundary values
remain unknown. We provide a characterization of the unknown boundary values
for the Dirichlet as well as the two Neumann problems in terms of a system of
nonlinear integral equations. The characterizations are effective in the sense
that the integral equations can be solved perturbatively to all orders in a
well-defined recursive scheme.
