Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
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dc.contributor.author	Witte, N.S.
dc.contributor.author	Ormerod, C.M.
dc.date.accessioned	2019-02-18T17:56:05Z
dc.date.available	2019-02-18T17:56:05Z
dc.date.issued	2012
dc.identifier.citation	Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System / N.S. Witte, C.M. Ormerod // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 18 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 39A05; 42C05; 34M55; 34M56; 33C45; 37K35
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2012.097
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148694
dc.description.abstract	We construct a Lax pair for the E₆⁽¹⁾ q-Painlevé system from first principles by employing the general theory of semi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic lattices [arXiv:1204.2328]. Our study treats one special case of such lattices - the q-linear lattice - through a natural generalisation of the big q-Jacobi weight. As a by-product of our construction we derive the coupled first-order q-difference equations for the E₆⁽¹⁾ q-Painlevé system, thus verifying our identification. Finally we establish the correspondences of our result with the Lax pairs given earlier and separately by Sakai and Yamada, through explicit transformations.	uk_UA
dc.description.sponsorship	This research has been supported by the Australian Research Council’s Centre of Excellence for Mathematics and Statistics of Complex Systems. We are grateful for the clarifications by Kenji Kajiwara of results given in [6] and [5] and the assistance of Yasuhiko Yamada in explaining the results of his work [18]. We also appreciate the assistance of Jason Whyte in the preparation of this manuscript.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA