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

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dc.contributor.author Grava, Tamara en_US
dc.contributor.author Klein, Christian en_US
dc.date.accessioned 2007-12-12T12:39:24Z en_US
dc.date.accessioned 2011-09-07T20:24:10Z
dc.date.available 2007-12-12T12:39:24Z en_US
dc.date.available 2011-09-07T20:24:10Z
dc.date.issued 2007-12-12T12:39:24Z en_US
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/2527 en_US
dc.description.abstract We 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 Painlev\'e 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 en_US
dc.format.extent 367188 bytes en_US
dc.format.mimetype application/pdf en_US
dc.language.iso en_US en_US
dc.relation.ispartofseries arXiv.org;math-ph/0702038v1 en_US
dc.title Numerical study of a multiscale expansion of KdV and Camassa-Holm equation en_US
dc.type Preprint en_US
dc.contributor.department Mathematical Physics en_US
dc.contributor.area Mathematics en_US


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