2013 Fiscal Year Final Research Report
Study on the integrable structure of ultradiscrete systems
| Project/Area Number |
21340034
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TOKIHIRO Tetsuji 東京大学, 数理(科)学研究科(研究院), 教授 (10163966)
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| Co-Investigator(Renkei-kenkyūsha) |
OKAMOTO Kazuo 東京大学, 大学院数理科学研究科, 名誉教授 (40011720)
UIROKKUSU Rarufu 東京大学, 大学院数理科学研究科, 准教授 (20361610)
SAKAI Hidetaka 東京大学, 大学院数理科学研究科, 准教授 (50323465)
IZUMI Makoto 島根大学, 教育学部, 教授 (50263497)
TAKENAWA Tomoyuki 東京海洋大学, 海洋工学部, 准教授 (70361805)
INOUE Rei 千葉大学, 理学部, 准教授 (30431901)
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| Project Period (FY) |
2009-04-01 – 2013-03-31
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| Keywords | セルオートマトン / 超離散系 / 可積分系 / 箱玉系 / 有限体 / トロピカル曲線 |
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| Research Abstract |
An ultradiscrete system denotes a cellular automaton constructed from a continuous equation through a limiting procedure. We investigated the ultradiscrete systems which are considered to have integrability. The principal results in this research are; (1) the correlation functions of the box-ball systems, which are typical integrable ultrtadiscrete systems, are obtained, (2) the mathematical structure of the so-called negative solitons in the ultradiscrete KdV equation is clarified, (3) solutions to ultradiscrete Painlevé equations are constructed and a series of formulae for partition numbers are obtained, (4) integrable systems over finite fields are shown to have a property called AGR (almost good reduction).
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