  The Korteweg de Vries (KdV) equation with small dispersion is a model for the
formation and propagation of dispersive shock waves in one dimension.
Dispersive shock waves in KdV are characterized by the appearance of zones of
rapid modulated oscillations in the solution of the Cauchy problem with smooth
initial data. The modulation in time and space of the amplitudes, the
frequencies and the wave-numbers of these oscillations and their interactions
is approximately described by the $g$-phase Whitham equations. We study the
initial value problem for the Whitham equations for a one parameter family of
monotone decreasing initial data. We obtain the bifurcation diagram of the
number $g$ of interacting oscillatory zones.
