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

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

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 d...

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Veröffentlicht in:Communications in mathematical sciences 2006, Vol.4 (4), p.799-822
Hauptverfasser: Pierce, Virgil U., Tian, Fei-Ran
Format: Artikel
Sprache:eng
Schlagworte:
35C05
35L65
35L67
35Q53
non-strictly hyperbolic equations
Whitham equations
Zero dispersion limit
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Zusammenfassung: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.
ISSN:1539-6746
1945-0796
DOI:10.4310/CMS.2006.v4.n4.a7