dorsal/arxiv
View SchemaCasorati Determinant Solutions for the Discrete Painlev\'e III Equation
| Authors | Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9412004 |
| URL | https://arxiv.org/abs/solv-int/9412004 |
| DOI | 10.1063/1.531353 |
Abstract
The discrete Painlev\'e III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel function. Moreover, based on the observation that these discrete Bessel functions are transformed to the $q$-Bessel functions by a simple variable transformation, we present a $q$-difference analogue of the Painlev\'e III equation.
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"abstract": "The discrete Painlev\\\u0027e III equation is investigated based on the bilinear\nformalism. It is shown that it admits the solutions expressed by the Casorati\ndeterminant whose entries are given by the discrete Bessel function. Moreover,\nbased on the observation that these discrete Bessel functions are transformed\nto the $q$-Bessel functions by a simple variable transformation, we present a\n$q$-difference analogue of the Painlev\\\u0027e III equation.",
"arxiv_id": "solv-int/9412004",
"authors": [
"Kenji Kajiwara",
"Yasuhiro Ohta",
"Junkichi Satsuma"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"doi": "10.1063/1.531353",
"title": "Casorati Determinant Solutions for the Discrete Painlev\\\u0027e III Equation",
"url": "https://arxiv.org/abs/solv-int/9412004"
},
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