Dynamics of Partial Differential Equations

Volume 4 (2007)

Number 3

Self-similar solutions of the non-strictly hyperbolic Whithamequations for the KdV hierarchy

Pages: 263 – 282

DOI: https://dx.doi.org/10.4310/DPDE.2007.v4.n3.a4

Authors

V. U. Pierce (Department of Mathematics, Ohio State University, Columbus, Ohio, U.S.A.)

Fei-Ran Tian (Department of Mathematics, Ohio State University, Columbus, Ohio, U.S.A.)

Abstract

We study the Whitham equations for all the higher order KdV equations. The Whitham 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.

Keywords

Whitham equations, KdV equation, self-similar solution, KdV hierarchy

2010 Mathematics Subject Classification

35-xx, 76-xx

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Published 1 January 2007