Hamiltonian Structure of PI Hierarchy
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Hamiltonian Structure of PI Hierarchy
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| Creator |
Takasaki, K.
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| 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).
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| Date |
2019-02-16T08:51:28Z
2019-02-16T08:51:28Z 2007 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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