Numerical study of a multiscale expansion of KdV and Camassa-Holm equation

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dc.creatorGrava, T.
dc.creatorKlein, C.
dc.date2007-02-12
dc.date.accessioned2026-07-07T07:46:15Z
dc.date.available2026-07-07T07:46:15Z
dc.descriptionWe study numerically solutions to the Korteweg-de Vries and Camassa-Holm equation close to the breakup of the corresponding solution to the dispersionless equation. The solutions are compared with the properly rescaled numerical solution to a fourth order ordinary differential equation, the second member of the Painlevé I hierarchy. It is shown that this solution gives a valid asymptotic description of the solutions close to breakup. We present a detailed analysis of the situation and compare the Korteweg-de Vries solution quantitatively with asymptotic solutions obtained via the solution of the Hopf and the Whitham equations. We give a qualitative analysis for the Camassa-Holm equation
dc.description17 pages, 13 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0702038
dc.identifierhttp://arxiv.org/abs/math-ph/0702038
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123770
dc.subjectMathematical Physics
dc.subject54C40, 14E20, 46E25, 20C20
dc.titleNumerical study of a multiscale expansion of KdV and Camassa-Holm equation
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