Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation
Exactly Solvable and Integrable Systems
2009-11-13 v1 Mathematical Physics
Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.0805.2558,
title = {Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation},
author = {Tamara Grava and V. U. Pierce and Fei-Ran Tian},
journal= {arXiv preprint arXiv:0805.2558},
year = {2009}
}
Comments
33 pages, 3 figures