| Project/Area Number |
12640169
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
TAKASAKI Kanehisa Kyoto Univ., Integrated Human Studies, Ass. Professor, 総合人間学部, 助教授 (40171433)
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| Co-Investigator(Kenkyū-buntansha) |
MATSUKI Toshihiko Kyoto Univ., Integrated Human Studies, Ass. Professor, 総合人間学部, 助教授 (20157283)
KATO Shinichi Kyoto Univ., Integrated Human Studies, Professor, 総合人間学部, 教授 (90114438)
UEDA Tetsuo Kyoto Univ., Integrated Human Studies, Professor, 総合人間学部, 教授 (10127053)
UEKI Naomasa Kyoto Univ., Graduate School of Human and Environmental Studies, Ass. Professor, 大学院・人間・環境研究科, 助教授 (80211069)
ASANO Kiyoshi Kyoto Univ., Graduate School of Human and Environmental Studies, Professor, 大学院・人間・環境研究科, 教授 (90026774)
宇敷 重広 京都大学, 大学院・人間・環境学研究科, 教授 (10093197)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,900,000)
Fiscal Year 2001: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2000: ¥2,400,000 (Direct Cost: ¥2,400,000)
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| Keywords | integrable system / isomonodromy / Painleve equation / spectral curve / separation of variables / Hamiltonian structure / quantum solvability / moduli space / 変数分離 / K3曲面 / 有理楕円曲面 / Calogero系 / Ruijsenaars系 |
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| Research Abstract |
1. The dressing chains are known to be an important nonlinear differential equation that includes the Painleve equations. These equations have a Lax representation by a second order square matrix, and the associated spectral curve becomes hyperelliptic. This enabled us to apply the technique of separation of variables, and to obtain a Hamiltonian representation of the dressing chains under a periodic boundary condition.
2. A non-autonomous version of the SU(2) Calogero-Gaudin system was taken up an example of isomonodromic deformations on a torus. We applied the technique of separation of variables to rewrite this system into a Hamiltonian form. As a byproduct, we could find a connection of this matrix system with a scalar isomonodromic system.
3. The Inozemtsev system is a deformation of the Calogero-Moser system retaining the classical integrability. We considered its quantum theory, and discovered that the quantum system has partial solvability (quasi-exact-solvability) at a discrete series of special values of one of the coupling constants.
4. The moduli space of a class of rational functions is known to carry the structure of an integrable system. We constructed a new integrable system by replacing the rational functions by trigonometric or elliptic functions, and pointed out that these integrable systems provide very simple models of separation of variables.
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