Isomonodromy and Painlevé Type Equations, Case Studies
There is an abundance of equations of Painlevé type besides the classical Painlevé equations. Classifications have been computed by the Japanese school. Here we consider Painlevé-type equations induced by isomonodromic families of linear ODE's having at most = 0 and = ∞ as singularities. Requ...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214093 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Isomonodromy and Painlevé Type Equations, Case Studies. Marius van der Put and Jaap Top. SIGMA 21 (2025), 075, 32 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862710530173566976 |
|---|---|
| author | van der Put, Marius Top, Jaap |
| author_facet | van der Put, Marius Top, Jaap |
| citation_txt | Isomonodromy and Painlevé Type Equations, Case Studies. Marius van der Put and Jaap Top. SIGMA 21 (2025), 075, 32 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | There is an abundance of equations of Painlevé type besides the classical Painlevé equations. Classifications have been computed by the Japanese school. Here we consider Painlevé-type equations induced by isomonodromic families of linear ODE's having at most = 0 and = ∞ as singularities. Requiring that the formal data at the singularities produce isomonodromic families parametrized by a single variable leads to a small list of hierarchies of cases. The study of these cases involves Stokes matricesand moduli for linear ODE's on the projective line. Case studies reveal interesting families of linear ODE's and Painlevé-type equations. However, rather often the complexity (especially of the Lax pair) is too high for either the computations or the output. Apart from classical Painlevé equations, one rediscovers the work of Harnad, Noumi, and Yamada. A hierarchy, probably new, related to the classical ₃(₈), is discovered. Finally, an amusing ''companion'' of ₁ is presented.
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| first_indexed | 2026-03-19T12:42:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214093 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T12:42:17Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | van der Put, Marius Top, Jaap 2026-02-19T11:11:37Z 2025 Isomonodromy and Painlevé Type Equations, Case Studies. Marius van der Put and Jaap Top. SIGMA 21 (2025), 075, 32 pages 1815-0659 2020 Mathematics Subject Classification: 33E17; 14D20; 14D22; 34M55 arXiv:2404.15767 https://nasplib.isofts.kiev.ua/handle/123456789/214093 https://doi.org/10.3842/SIGMA.2025.075 There is an abundance of equations of Painlevé type besides the classical Painlevé equations. Classifications have been computed by the Japanese school. Here we consider Painlevé-type equations induced by isomonodromic families of linear ODE's having at most = 0 and = ∞ as singularities. Requiring that the formal data at the singularities produce isomonodromic families parametrized by a single variable leads to a small list of hierarchies of cases. The study of these cases involves Stokes matricesand moduli for linear ODE's on the projective line. Case studies reveal interesting families of linear ODE's and Painlevé-type equations. However, rather often the complexity (especially of the Lax pair) is too high for either the computations or the output. Apart from classical Painlevé equations, one rediscovers the work of Harnad, Noumi, and Yamada. A hierarchy, probably new, related to the classical ₃(₈), is discovered. Finally, an amusing ''companion'' of ₁ is presented. We thank the referees for their work and suggestions, resulting in a considerable revision of an earlier version of this text. We especially thank Anton Dzhamay for his successful effort to identify two of the Painlevé-type equations obtained in this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Isomonodromy and Painlevé Type Equations, Case Studies Article published earlier |
| spellingShingle | Isomonodromy and Painlevé Type Equations, Case Studies van der Put, Marius Top, Jaap |
| title | Isomonodromy and Painlevé Type Equations, Case Studies |
| title_full | Isomonodromy and Painlevé Type Equations, Case Studies |
| title_fullStr | Isomonodromy and Painlevé Type Equations, Case Studies |
| title_full_unstemmed | Isomonodromy and Painlevé Type Equations, Case Studies |
| title_short | Isomonodromy and Painlevé Type Equations, Case Studies |
| title_sort | isomonodromy and painlevé type equations, case studies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214093 |
| work_keys_str_mv | AT vanderputmarius isomonodromyandpainlevetypeequationscasestudies AT topjaap isomonodromyandpainlevetypeequationscasestudies |