  The generation of an undular bore in the vicinity of a wave-breaking point is
considered for the integrable Kaup-Boussinesq shallow water system. In the
framework of the Whitham modulation theory, an analytic solution of the
Gurevich-Pitaevskii type of problem for a generic "cubic" breaking regime is
obtained using a generalized hodograph transform, and a further reduction to a
linear Euler-Poisson equation. The motion of the undular bore edges is
investigated in detail.
