dorsal/arxiv
View SchemaThe hunting for the discrete Painlev\'e VI is over
| Authors | B. Grammaticos, A. Ramani |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9901006 |
| URL | https://arxiv.org/abs/solv-int/9901006 |
Abstract
We present the discrete, q-, form of the Painlev\'e VI equation written as a three-point mapping and analyse the structure of its singularities. This discrete equation goes over to P_{VI} at the continuous limit and degenerates towards the discrete q-P_{V} through coalescence. It possesses special solutions in terms of the q-hypergeometric function. It can bilinearised and, under the appropriate assumptions, ultradiscretised. A new discrete form for P_{V} is also obtained which is of difference type, in contrast with the `standard' form of the discrete P_{V}. Finally, we present the `asymmetric' form of q-P_{VI}$ as a system of two first-order mappings involving seven arbitrary parameters.
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"abstract": "We present the discrete, q-, form of the Painlev\\\u0027e VI equation written as a\nthree-point mapping and analyse the structure of its singularities. This\ndiscrete equation goes over to P_{VI} at the continuous limit and degenerates\ntowards the discrete q-P_{V} through coalescence. It possesses special\nsolutions in terms of the q-hypergeometric function. It can bilinearised and,\nunder the appropriate assumptions, ultradiscretised. A new discrete form for\nP_{V} is also obtained which is of difference type, in contrast with the\n`standard\u0027 form of the discrete P_{V}. Finally, we present the `asymmetric\u0027\nform of q-P_{VI}$ as a system of two first-order mappings involving seven\narbitrary parameters.",
"arxiv_id": "solv-int/9901006",
"authors": [
"B. Grammaticos",
"A. Ramani"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "The hunting for the discrete Painlev\\\u0027e VI is over",
"url": "https://arxiv.org/abs/solv-int/9901006"
},
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