Extension of special functions from the viewpoint of integrable systems
| Project/Area Number |
23540252
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Rikkyo University |
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Principal Investigator |
KAKEI Saburo 立教大学, 理学部, 教授 (60318798)
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| Co-Investigator(Renkei-kenkyūsha) |
SAITO Yoshihisa 東京大学, 数理科学研究科, 准教授 (20294522)
WILLOX Ralph 東京大学, 数理科学研究科, 教授 (20361610)
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 可積分系 / 特殊関数 / ソリトン / 超離散化 |
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| Outline of Final Research Achievements |
This research project aims to extend the theory of integrable systems and special functions. We have focused mainly on applications to differential geometry and combinatorics, and obtained the following results;
(1) Goldstein and Petrich introduced a hierarchy of equations that governs isoperimetric deformation of plane curves. We have revealed that the Goldstein-Petrich hierarchy is indeed a reduced case of the Toda lattice hierarchy. (2) We have studied rigged configurations from the viewpoint of soliton cellular automaton. We have obtained alternative proof of the linearization property of the time-evolution, which is simpler than the known proofs.
We have obtained still other preliminary results that are related to applications of integrable systems to differential geometry and combinatorics. We will investigate them further in near future.
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Report
(6 results)
Research Products
(33 results)
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[Presentation] 平面渦の定常配置と安定性2014
Author(s)
上野拓，筧三郎
Organizer
非線形波動研究の現状 ―課題と展望を探る―
Place of Presentation
九州大学応用力学研究所（福岡県春日市）
Year and Date
2014-10-31
Related Report
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