dorsal/arxiv
View SchemaThe KdV equation on a half-line
| Authors | I. T. Habibullin, A. N. Vil'danov |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9910002 |
| URL | https://arxiv.org/abs/solv-int/9910002 |
Abstract
The initial boundary value problem on a half-line for the KdV equation with the boundary conditions $u|_{x=0}=a\leq0$, $u_{xx}|_{x=0}=3a^2$ is integrated by means of the inverse scattering method. In order to find the time evolution of the scattering matrix it turned out to be sufficient to solve the Riemann problem on a hyperelliptic curve of genus two, where the conjugation matrices are effectively defined by initial data.
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"abstract": "The initial boundary value problem on a half-line for the KdV equation with\nthe boundary conditions $u|_{x=0}=a\\leq0$, $u_{xx}|_{x=0}=3a^2$ is integrated\nby means of the inverse scattering method. In order to find the time evolution\nof the scattering matrix it turned out to be sufficient to solve the Riemann\nproblem on a hyperelliptic curve of genus two, where the conjugation matrices\nare effectively defined by initial data.",
"arxiv_id": "solv-int/9910002",
"authors": [
"I. T. Habibullin",
"A. N. Vil\u0027danov"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "The KdV equation on a half-line",
"url": "https://arxiv.org/abs/solv-int/9910002"
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