Numerical solution of the small dispersion limit of Korteweg de Vries and Whitham equations
| 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 | 2005 | en_US |
| dc.date.accessioned | 2011-09-07T20:28:34Z | |
| dc.date.available | 2005 | en_US |
| dc.date.available | 2011-09-07T20:28:34Z | |
| dc.date.issued | 2005 | en_US |
| dc.description.abstract | The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\epsilon^2$, is characterized by the appearance of a zone of rapid modulated oscillations of wave-length of order $\epsilon$. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. In this manuscript we give a quantitative analysis of the discrepancy between the numerical solution of the KdV equation in the small dispersion limit and the corresponding approximate solution for values of $\epsilon$ between $10^{-1}$ and $10^{-3}$. The numerical results are compatible with a difference of order $\epsilon$ within the `interior' of the Whitham oscillatory zone, of order $\epsilon^{1/3}$ at the left boundary outside the Whitham zone and of order $\epsilon^{1/2}$ at the right boundary outside the Whitham zone. | en_US |
| dc.format.extent | 905542 bytes | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | Comm. Pure Appl. Math. 60 (2007) 1623-1664 | en_US |
| dc.identifier.uri | https://openscience.sissa.it/handle/1963/1788 | en_US |
| dc.language.iso | en_US | en_US |
| dc.relation.ispartofseries | SISSA;91/2005/FM | en_US |
| dc.relation.ispartofseries | arXiv.org;math-ph/0511011 | en_US |
| dc.relation.uri | 10.1002/cpa.20183 | en_US |
| dc.title | Numerical solution of the small dispersion limit of Korteweg de Vries and Whitham equations | en_US |
| dc.type | Preprint | en_US |