dorsal/arxiv
View SchemaBilinear Discrete Painleve-II and its Particular Solutions
| Authors | J. Satsuma, K. Kajiwara, B. Grammaticos, J. Hietarinta, A. Ramani |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9412007 |
| URL | https://arxiv.org/abs/solv-int/9412007 |
| DOI | 10.1088/0305-4470/28/12/025 |
Abstract
By analogy to the continuous Painlev\'e II equation, we present particular solutions of the discrete Painlev\'e II (d-P$\rm_{II}$) equation. These solutions are of rational and special function (Airy) type. Our analysis is based on the bilinear formalism that allows us to obtain the $\tau$ function for d-P$\rm_{II}$. Two different forms of bilinear d-P$\rm_{II}$ are obtained and we show that they can be related by a simple gauge transformation.
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"abstract": "By analogy to the continuous Painlev\\\u0027e II equation, we present particular\nsolutions of the discrete Painlev\\\u0027e II (d-P$\\rm_{II}$) equation. These\nsolutions are of rational and special function (Airy) type. Our analysis is\nbased on the bilinear formalism that allows us to obtain the $\\tau$ function\nfor d-P$\\rm_{II}$. Two different forms of bilinear d-P$\\rm_{II}$ are obtained\nand we show that they can be related by a simple gauge transformation.",
"arxiv_id": "solv-int/9412007",
"authors": [
"J. Satsuma",
"K. Kajiwara",
"B. Grammaticos",
"J. Hietarinta",
"A. Ramani"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0305-4470/28/12/025",
"title": "Bilinear Discrete Painleve-II and its Particular Solutions",
"url": "https://arxiv.org/abs/solv-int/9412007"
},
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