Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System
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 lat...
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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148694 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148694 |
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irk-123456789-1486942019-02-19T01:27:25Z Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System Witte, N.S. Ormerod, C.M. 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. 2012 Article 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. 1815-0659 2010 Mathematics Subject Classification: 39A05; 42C05; 34M55; 34M56; 33C45; 37K35 DOI: http://dx.doi.org/10.3842/SIGMA.2012.097 http://dspace.nbuv.gov.ua/handle/123456789/148694 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 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. |
| format |
Article |
| author |
Witte, N.S. Ormerod, C.M. |
| spellingShingle |
Witte, N.S. Ormerod, C.M. Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Witte, N.S. Ormerod, C.M. |
| author_sort |
Witte, N.S. |
| title |
Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System |
| title_short |
Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System |
| title_full |
Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System |
| title_fullStr |
Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System |
| title_full_unstemmed |
Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System |
| title_sort |
construction of a lax pair for the e₆⁽¹⁾ q-painlevé system |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148694 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:31:12Z |
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2023-05-20T17:31:12Z |
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