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The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I

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dc.contributor.author Ormerod, C.M.
dc.date.accessioned 2019-02-11T18:05:42Z
dc.date.available 2019-02-11T18:05:42Z
dc.date.issued 2011
dc.identifier.citation The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I / C.M. Ormerod // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 34M55; 39A13
dc.identifier.other DOI:10.3842/SIGMA.2011.045
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/146862
dc.description.abstract We wish to explore a link between the Lax integrability of the q-Painlevé equations and the symmetries of the q-Painlevé equations. We shall demonstrate that the connection preserving deformations that give rise to the q-Painlevé equations may be thought of as elements of the groups of Schlesinger transformations of their associated linear problems. These groups admit a very natural lattice structure. Each Schlesinger transformation induces a Bäcklund transformation of the q-Painlevé equation. Each translational Bäcklund transformation may be lifted to the level of the associated linear problem, effectively showing that each translational Bäcklund transformation admits a Lax pair. We will demonstrate this framework for the q-Painlevé equations up to and including q-PVI. 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 The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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