Open Access
December 2006 Self-similar solutions of the non-strictly hyperbolic Whitham equations
Virgil U. Pierce, Fei-Ran Tian
Commun. Math. Sci. 4(4): 799-822 (December 2006).


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.


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Virgil U. Pierce. Fei-Ran Tian. "Self-similar solutions of the non-strictly hyperbolic Whitham equations." Commun. Math. Sci. 4 (4) 799 - 822, December 2006.


Published: December 2006
First available in Project Euclid: 5 April 2007

MathSciNet: MR2264821
zbMATH: 1133.35086

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

Keywords: non-strictly hyperbolic equations , Whitham equations , zero dispersion limit

Rights: Copyright © 2006 International Press of Boston

Vol.4 • No. 4 • December 2006
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