Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations

Details Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations

2006-07-27

arxiv.org/abs/nlin/0607061v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

38 pages, 8 figures

Scientific paper

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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