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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148694 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862720885815771136 |
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| author | Witte, N.S. Ormerod, C.M. |
| author_facet | Witte, N.S. Ormerod, C.M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T18:27:53Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148694 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:27:53Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
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| spelling | Witte, N.S. Ormerod, C.M. 2019-02-18T17:56:05Z 2019-02-18T17:56:05Z 2012 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 https://nasplib.isofts.kiev.ua/handle/123456789/148694 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. This research has been supported by the Australian Research Council’s Centre of Excellence for Mathematics and Statistics of Complex Systems. We are grateful for the clarifications by Kenji Kajiwara of results given in [6] and [5] and the assistance of Yasuhiko Yamada in explaining the results of his work [18]. We also appreciate the assistance of Jason Whyte in the preparation of this manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System Article published earlier |
| spellingShingle | Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System Witte, N.S. Ormerod, C.M. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148694 |
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