Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation
A multi-Poisson structure on a Lie algebra g provides a systematic way to construct completely integrable Hamiltonian systems on g expressed in Lax form ∂Xλ/∂t=[Xλ,Aλ] in the sense of the isospectral deformation, where Xλ,Aλ∈g depend rationally on the indeterminate λ called the spectral parameter. I...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2017 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2017
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148562 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation / H. Chiba // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 18 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862715314580488192 |
|---|---|
| author | Chiba, H. |
| author_facet | Chiba, H. |
| citation_txt | Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation / H. Chiba // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A multi-Poisson structure on a Lie algebra g provides a systematic way to construct completely integrable Hamiltonian systems on g expressed in Lax form ∂Xλ/∂t=[Xλ,Aλ] in the sense of the isospectral deformation, where Xλ,Aλ∈g depend rationally on the indeterminate λ called the spectral parameter. In this paper, a method for modifying the isospectral deformation equation to the Lax equation ∂Xλ/∂t=[Xλ,Aλ]+∂Aλ/∂λ in the sense of the isomonodromic deformation, which exhibits the Painlevé property, is proposed. This method gives a few new Painlevé systems of dimension four.
|
| first_indexed | 2025-12-07T17:57:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148562 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:57:29Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chiba, H. 2019-02-18T15:51:51Z 2019-02-18T15:51:51Z 2017 Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation / H. Chiba // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 18 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34M35; 34M45; 34M55 DOI:10.3842/SIGMA.2017.025 https://nasplib.isofts.kiev.ua/handle/123456789/148562 A multi-Poisson structure on a Lie algebra g provides a systematic way to construct completely integrable Hamiltonian systems on g expressed in Lax form ∂Xλ/∂t=[Xλ,Aλ] in the sense of the isospectral deformation, where Xλ,Aλ∈g depend rationally on the indeterminate λ called the spectral parameter. In this paper, a method for modifying the isospectral deformation equation to the Lax equation ∂Xλ/∂t=[Xλ,Aλ]+∂Aλ/∂λ in the sense of the isomonodromic deformation, which exhibits the Painlevé property, is proposed. This method gives a few new Painlevé systems of dimension four. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation Article published earlier |
| spellingShingle | Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation Chiba, H. |
| title | Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation |
| title_full | Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation |
| title_fullStr | Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation |
| title_full_unstemmed | Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation |
| title_short | Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation |
| title_sort | multi-poisson approach to the painlevé equations: from the isospectral deformation to the isomonodromic deformation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148562 |
| work_keys_str_mv | AT chibah multipoissonapproachtothepainleveequationsfromtheisospectraldeformationtotheisomonodromicdeformation |