Hamiltonian Structure of PI Hierarchy
The string equation of type (2,2g+1) may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called th...
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| Дата: | 2007 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147820 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Hamiltonian Structure of PI Hierarchy / K. Takasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 41 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1478202019-02-17T01:23:38Z Hamiltonian Structure of PI Hierarchy Takasaki, K. The string equation of type (2,2g+1) may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can be introduced in this hierarchy as well. The equations of motion in these Darboux coordinates turn out to take a Hamiltonian form, but the Hamiltonians are different from the Hamiltonians of the Lax equations (except for the lowest one that corresponds to the string equation itself). 2007 Article Hamiltonian Structure of PI Hierarchy / K. Takasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 41 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 34M55; 35Q53; 37K20 http://dspace.nbuv.gov.ua/handle/123456789/147820 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 |
The string equation of type (2,2g+1) may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can be introduced in this hierarchy as well. The equations of motion in these Darboux coordinates turn out to take a Hamiltonian form, but the Hamiltonians are different from the Hamiltonians of the Lax equations (except for the lowest one that corresponds to the string equation itself). |
| format |
Article |
| author |
Takasaki, K. |
| spellingShingle |
Takasaki, K. Hamiltonian Structure of PI Hierarchy Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Takasaki, K. |
| author_sort |
Takasaki, K. |
| title |
Hamiltonian Structure of PI Hierarchy |
| title_short |
Hamiltonian Structure of PI Hierarchy |
| title_full |
Hamiltonian Structure of PI Hierarchy |
| title_fullStr |
Hamiltonian Structure of PI Hierarchy |
| title_full_unstemmed |
Hamiltonian Structure of PI Hierarchy |
| title_sort |
hamiltonian structure of pi hierarchy |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147820 |
| citation_txt |
Hamiltonian Structure of PI Hierarchy / K. Takasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 41 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT takasakik hamiltonianstructureofpihierarchy |
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2023-05-20T17:28:35Z |
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2023-05-20T17:28:35Z |
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