Characteristic properties of the scattering data for the mKdV equation on the half-line
| dc.creator | de Monvel, Anne Boutet | |
| dc.creator | Kotlyarov, Vladimir | |
| dc.date | 2003-07-14 | |
| dc.date.accessioned | 2026-07-07T04:59:39Z | |
| dc.date.available | 2026-07-07T04:59:39Z | |
| dc.description | In this paper we describe characteristic properties of the scattering data of the compatible eigenvalue problem for the pair of differential equations related to the modified Korteweg-de Vries (mKdV) equation whose solution is defined in some half-strip $(0<x<\infty)\times[0,T]$, or in the quarter plane $(0<x<\infty)\times(0<t<\infty)$. We suppose that this solution has a $C^{\infty}$ initial function vanishing as $x\to\infty$, and $C^{\infty}$ boundary values, vanishing as $t\to\infty$ when $T=\infty$. We study the corresponding scattering problem for the compatible Zakharov-Shabat system of differential equations associated with the mKdV equation and obtain a representation of the solution of the mKdV equation through Marchenko integral equations of the inverse scattering method. The kernel of these equations is valid only for $x\geq 0$ and it takes into account all specific properties of the pair of compatible differential equations in the chosen half-strip or in the quarter plane. The main result is the collection A-B-C of characteristic properties of the scattering functions given in the paper. | |
| dc.description | LaTeX, 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/0307191 | |
| dc.identifier | http://arxiv.org/abs/math/0307191 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68070 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 37K15, 35Q53 | |
| dc.title | Characteristic properties of the scattering data for the mKdV equation on the half-line | |
| dc.type | text |