The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I
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| Creator |
Ormerod, C.M.
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| Description |
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.
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| Date |
2019-02-11T18:05:42Z
2019-02-11T18:05:42Z 2011 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 34M55; 39A13 DOI:10.3842/SIGMA.2011.045 http://dspace.nbuv.gov.ua/handle/123456789/146862 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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