Numerical study of a multiscale expansion of KdV and Camassa-Holm equation
| dc.contributor.area | Mathematics | 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 | 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.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.identifier.uri | https://openscience.sissa.it/handle/1963/2527 | 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 |