dorsal/arxiv
View SchemaCasorati Determinant Solutions for the Discrete Painlev\'e-II Equation
| Authors | Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma, Basil Grammaticos, Alfred Ramani |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9310002 |
| URL | https://arxiv.org/abs/solv-int/9310002 |
| DOI | 10.1088/0305-4470/27/3/030 |
Abstract
We present a class of solutions to the discrete Painlev\'e-II equation for particular values of its parameters. It is shown that these solutions can be expressed in terms of Casorati determinants whose entries are discrete Airy functions. The analogy between the $\tau$ function for the discrete P$_{\rm \romanno2}$ and the that of the discrete Toda molecule equation is pointed out.
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"abstract": "We present a class of solutions to the discrete Painlev\\\u0027e-II equation for\nparticular values of its parameters. It is shown that these solutions can be\nexpressed in terms of Casorati determinants whose entries are discrete Airy\nfunctions. The analogy between the $\\tau$ function for the discrete P$_{\\rm\n\\romanno2}$ and the that of the discrete Toda molecule equation is pointed out.",
"arxiv_id": "solv-int/9310002",
"authors": [
"Kenji Kajiwara",
"Yasuhiro Ohta",
"Junkichi Satsuma",
"Basil Grammaticos",
"Alfred Ramani"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0305-4470/27/3/030",
"title": "Casorati Determinant Solutions for the Discrete Painlev\\\u0027e-II Equation",
"url": "https://arxiv.org/abs/solv-int/9310002"
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