%0 Journal Article
%J Physica D 238 (2009) 55-66
%D 2009
%T Initial value problem of the Whitham equations for the Camassa-Holm equation
%A Tamara Grava
%A Virgil U. Pierce
%A Fei-Ran Tian
%X 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.
%B Physica D 238 (2009) 55-66
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/3429
%1 906
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-13T13:01:16Z\\nNo. of bitstreams: 1\\n0805.2558v1.pdf: 498872 bytes, checksum: 4d721f99d6ae9840be2332f3cc6a4118 (MD5)
%R 10.1016/j.physd.2008.08.016