dorsal/arxiv
View SchemaOn an integrable discretization of the modified Korteweg-de Vries equation
| Authors | Yuri B. Suris |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9702003 |
| URL | https://arxiv.org/abs/solv-int/9702003 |
| DOI | 10.1016/S0375-9601(97)00592-6 |
| Journal | Phys. Lett. A, 1997, V.234, p. 91-102. |
Abstract
We find time discretizations for the two ''second flows'' of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one-field reduction and serve therefore as valid space-time discretizations of the modified Korteweg-de Vries equation. We expect the performance of these discretizations to be much better then that of the Taha-Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well as the solution of an initial value problem in terms of matrix factorizations.
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"abstract": "We find time discretizations for the two \u0027\u0027second flows\u0027\u0027 of the\nAblowitz-Ladik hierachy. These discretizations are described by local equations\nof motion, as opposed to the previously known ones, due to Taha and Ablowitz.\nCertain superpositions of our maps allow a one-field reduction and serve\ntherefore as valid space-time discretizations of the modified Korteweg-de Vries\nequation. We expect the performance of these discretizations to be much better\nthen that of the Taha-Ablowitz scheme. The way of finding interpolating\nHamiltonians for our maps is also indicated, as well as the solution of an\ninitial value problem in terms of matrix factorizations.",
"arxiv_id": "solv-int/9702003",
"authors": [
"Yuri B. Suris"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/S0375-9601(97)00592-6",
"journal_ref": "Phys. Lett. A, 1997, V.234, p. 91-102.",
"title": "On an integrable discretization of the modified Korteweg-de Vries equation",
"url": "https://arxiv.org/abs/solv-int/9702003"
},
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