Commutation Relations and Discrete Garnier Systems
We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discr...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148532 |
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| Zitieren: | Commutation Relations and Discrete Garnier Systems / C. M. Ormerod, E. M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 56 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862618888113487872 |
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| author | Ormerod, C.M. Rains, E.M. |
| author_facet | Ormerod, C.M. Rains, E.M. |
| citation_txt | Commutation Relations and Discrete Garnier Systems / C. M. Ormerod, E. M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 56 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discrete isomonodromic deformations is completely determined by commutation relations between the factors. We also reparameterize these systems in terms of the image and kernel vectors at singular points to obtain a separate birational form. A distinguishing feature of this study is the presence of a symmetry condition on the associated linear problems that only appears as a necessary feature of the Lax pairs for the least degenerate discrete Painlevé equations.
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| first_indexed | 2025-12-07T13:15:48Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148532 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:15:48Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ormerod, C.M. Rains, E.M. 2019-02-18T14:48:18Z 2019-02-18T14:48:18Z 2016 Commutation Relations and Discrete Garnier Systems / C. M. Ormerod, E. M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 56 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 39A10; 39A13; 37K15 DOI:10.3842/SIGMA.2016.110 https://nasplib.isofts.kiev.ua/handle/123456789/148532 We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discrete isomonodromic deformations is completely determined by commutation relations between the factors. We also reparameterize these systems in terms of the image and kernel vectors at singular points to obtain a separate birational form. A distinguishing feature of this study is the presence of a symmetry condition on the associated linear problems that only appears as a necessary feature of the Lax pairs for the least degenerate discrete Painlevé equations. The work of EMR was partially supported by the National Science Foundation under the grant
 DMS-1500806. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Commutation Relations and Discrete Garnier Systems Article published earlier |
| spellingShingle | Commutation Relations and Discrete Garnier Systems Ormerod, C.M. Rains, E.M. |
| title | Commutation Relations and Discrete Garnier Systems |
| title_full | Commutation Relations and Discrete Garnier Systems |
| title_fullStr | Commutation Relations and Discrete Garnier Systems |
| title_full_unstemmed | Commutation Relations and Discrete Garnier Systems |
| title_short | Commutation Relations and Discrete Garnier Systems |
| title_sort | commutation relations and discrete garnier systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148532 |
| work_keys_str_mv | AT ormerodcm commutationrelationsanddiscretegarniersystems AT rainsem commutationrelationsanddiscretegarniersystems |