  We study the Whitham equations for the defocusing complex modified KdV (mKdV)
equation. These Whitham equations are quasilinear hyperbolic equations and they
describe the averaged dynamics of the rapid oscillations which appear in the
solution of the mKdV equation when the dispersive parameter is small. The
oscillations are referred to as dispersive shocks. The Whitham equations for
the mKdV equation are neither strictly hyperbolic nor genuinely nonlinear. We
are interested in the solutions of the Whitham equations when the initial
values are given by a step function. We also compare the results with those of
the defocusing nonlinear Schrodinger (NLS) equation. For the NLS equation, the
Whitham equations are strictly hyperbolic and genuinely nonlinear. We show that
the weak hyperbolicity of the mKdV-Whitham equations is responsible for an
additional structure in the dispersive shocks which has not been found in the
NLS case.
