2003 Fiscal Year Final Research Report Summary
Integrable systems with higher genus spectral parameter
| Project/Area Number |
14540172
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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., Graduate School of Human and Environmental Studies, Professor, 大学院・人間・環境学研究科, 教授 (40171433)
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| Co-Investigator(Kenkyū-buntansha) |
SASAKI Ryu Kyoto Univ., Yukawa Institute for Theoretical Physics, Ass.Professor, 基礎物理学研究所, 助教授 (20154007)
TAKEBE Takashi Ochanomizu Women's University, Department of Mathematics, Ass.Professor, 理学部, 助教授 (60240727)
IKEDA Takeshi Okayama Science University, Department of Applied Mathematics, Lecture, 理学部, 講師 (40309539)
UEKI Naomasa Kyoto Univ., Graduate School of Human and Environmental Studies, Ass.Professor, 大学院・人間・環境学研究科, 助教授 (80211069)
UE Masaaki Kyoto Univ., Graduate School of Science, Ass.Professor, 大学院・理学研究科, 助教授 (80134443)
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| Project Period (FY) |
2002 – 2003
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| Keywords | integrable system / soliton equation / algebraic curve / higher genus / vector bundle / Tyurin parameter / Grassmann manifold |
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| Research Abstract |
There has been progress in several different aspects as follows.
1.Soliton equations related to Tyurin parameters: Following Krichever's recent proposal on a construction of integrable systems with Tyurin parameters, we constructed an elliptic analogue of the nonlinear Schroedinger equation. It turned out that this equation, like many other soliton equations, can be mapped to a dynamical system on a submanifold of an infinite dimensional Grassmann manifold. This result result can be to an algebraic curve of arbitrary genus.
2. Landau-Lifshitz equation and infinite dimensional Grassmann variety: The Landau-Lifshitz equation is a typical soliton equation related to an elliptic curve. We found that this equation, too, can be interpreted as a dynamical system on a submanifold of an infinite dimensional Grassmann manifold.
3.Integrable system formulated by a pair of meromorphic functions on an algebraic curve of arbitrary genus: We constructed an integrable system on the moduli space of a pair of meromorphic functions on an algebraic curve of arbitrary genus. This system may be thought of as a special case of the so called Beauville system.
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