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Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions

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dc.contributor.author Abenda, Simonetta en_US
dc.contributor.author Grava, Tamara en_US
dc.contributor.author Klein, Christian en_US
dc.date.accessioned 2010-02-05T10:20:57Z en_US
dc.date.accessioned 2011-09-07T20:19:52Z
dc.date.available 2010-02-05T10:20:57Z en_US
dc.date.available 2011-09-07T20:19:52Z
dc.date.issued 2010-02-05T10:20:57Z en_US
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/3840 en_US
dc.description.abstract The small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture.... en_US
dc.format.extent 613403 bytes en_US
dc.format.mimetype application/pdf en_US
dc.language.iso en_US en_US
dc.relation.ispartofseries SISSA;10/2010/FM en_US
dc.relation.ispartofseries arXiv.org;0909.1020 en_US
dc.title Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions en_US
dc.type Preprint en_US
dc.contributor.department Mathematical Physics en_US
dc.contributor.area Mathematics en_US


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