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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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146862 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1468622019-02-12T01:24:34Z The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I Ormerod, C.M. 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. 2011 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Ormerod, C.M. |
| spellingShingle |
Ormerod, C.M. The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ormerod, C.M. |
| author_sort |
Ormerod, C.M. |
| title |
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_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_sort |
lattice structure of connection preserving deformations for q-painlevé equations i |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146862 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:25:53Z |
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2023-05-20T17:25:53Z |
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