2011 Fiscal Year Final Research Report
Direct methods for ultradiscrete systems
| Project/Area Number |
21540210
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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 |
Global analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
WILLOX Ralph 東京大学, 大学院・数理科学研究科, 准教授 (20361610)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 可積分系 / セル・オートマトン / 超離散系 / 離散系 |
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| Research Abstract |
Studying the algebraic structure of so-called discrete integrable systems-which can be obtained from continuous integrable systems by appropriate discretisation techniques-it proved possible to elucidate the symmetry structure of certain cellular automata known as "ultradiscrete integrable systems". As a result I obtained a novel technique for solving the so-called ultradiscrete KdV equation, which is the prototypical ultradiscrete integrable system. Moreover, the classification of certain types of discrete integrable systems not only led to the discovery of unexpected relations among them, but also, in the lower dimensional case, to extensions of the geometric structures of previously known discrete integrable systems to several new classes of discrete systems.
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