The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I
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 t...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146862 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862639103914278912 |
|---|---|
| author | Ormerod, C.M. |
| author_facet | Ormerod, C.M. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-01T00:29:26Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146862 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T00:29:26Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ormerod, C.M. 2019-02-11T18:05:42Z 2019-02-11T18:05:42Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/146862 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I Article published earlier |
| spellingShingle | The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I Ormerod, C.M. |
| title | The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I |
| title_full | The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I |
| title_fullStr | The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I |
| title_full_unstemmed | The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I |
| title_short | The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I |
| title_sort | lattice structure of connection preserving deformations for q-painlevé equations i |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146862 |
| work_keys_str_mv | AT ormerodcm thelatticestructureofconnectionpreservingdeformationsforqpainleveequationsi AT ormerodcm latticestructureofconnectionpreservingdeformationsforqpainleveequationsi |