Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions
| dc.contributor.area | Mathematics | en_US |
| dc.contributor.author | Abenda, Simonetta | en_US |
| dc.contributor.author | Grava, Tamara | en_US |
| dc.contributor.author | Klein, Christian | en_US |
| dc.contributor.department | Mathematical Physics | 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.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.identifier.uri | https://openscience.sissa.it/handle/1963/3840 | 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 |