Communications in Mathematical Sciences

Volume 4 (2006)

Number 4

Self-similar solutions of the non-strictly hyperbolic Whitham equations

Pages: 799 – 822

DOI: http://dx.doi.org/10.4310/CMS.2006.v4.n4.a7

Authors

Virgil U. Pierce

Fei-Ran Tian

Abstract

We study the Whitham equations for the fifth order KdV equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the solution of the Whitham equations when the initial values are given by a step function. We classify the step-like initial data into eight different types. We construct self-similar solutions for each type.

Keywords

Zero dispersion limit; Whitham equations; non-strictly hyperbolic equations

2010 Mathematics Subject Classification

Primary 35Q53. Secondary 35C05, 35L65, 35L67.

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