@article {2009,
title = {Initial value problem of the Whitham equations for the Camassa-Holm equation},
journal = {Physica D 238 (2009) 55-66},
number = {arXiv.org;0805.2558v1},
year = {2009},
publisher = {Elsevier},
abstract = {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.},
doi = {10.1016/j.physd.2008.08.016},
url = {http://hdl.handle.net/1963/3429},
author = {Tamara Grava and Virgil U. Pierce and Fei-Ran Tian}
}