  We study the Whitham equations for the Camassa-Holm equation. The equations
are neither strictly hyperbolic nor genuinely nonlinear. We are interested in
the initial value problem of the Whitham equations. When the initial values are
given by a step function, the Whitham solution is self-similar. When the
initial values are given by a smooth function, the Whitham solution exists
within a cusp in the x-t plane. On the boundary of the cusp, the Whitham
equation matches the Burgers solution, which exists outside the cusp.
