00963nas a2200133   4500008004300000245008100043210006900124260001300193520052900206100001800735700002200753700001800775856003600793       2009                        en_Ud  00aInitial value problem of the Whitham equations for the Camassa-Holm equation0 aInitial value problem of the Whitham equations for the CamassaHo  bElsevier3 aWe 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.1 aGrava, Tamara1 aPierce, Virgil U.1 aTian, Fei-Ran  uhttp://hdl.handle.net/1963/3429