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Initial value problem of the Whitham equations for the Camassa-Holm equation

TitleInitial value problem of the Whitham equations for the Camassa-Holm equation
Publication TypeJournal Article
Year of Publication2009
AuthorsGrava, T, Pierce, VU, Tian, F-R
JournalPhysica D 238 (2009) 55-66
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.

URLhttp://hdl.handle.net/1963/3429
DOI10.1016/j.physd.2008.08.016

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