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On a novel q-discrete analogue of the Painlevé VI equation

✍ Scribed by B. Grammaticos; A. Ramani

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
61 KB
Volume
257
Category
Article
ISSN
0375-9601

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✦ Synopsis

We present the discrete, q-, form of the Painleve VI equation written as a three-point mapping and analyse the structure óf its singularities. This discrete equation goes over to P at the continuous limit and degenerates towards the discrete q-P VI 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 is also obtained which is of difference type, in V contrast with the 'standard' form of the discrete P . Finally, we present the 'asymmetric' form of q-P as a system of two V V I first-order mappings involving seven arbitrary parameters.

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