  We show that the long-time behavior of solutions to the Korteweg-de Vries
shock problem can be described as a slowly modulated one-gap solution in the
dispersive shock region. The modulus of the elliptic function (i.e., the
spectrum of the underlying Schr\"odinger operator) depends only on the size of
the step of the initial data and on the direction, $\frac{x}{t}=const.$, along
which we determine the asymptotic behavior of the solution. In turn, the phase
shift (i.e., the Dirichlet spectrum) in this elliptic function depends also on
the scattering data, and is computed explicitly via the Jacobi inversion
problem.
