Towards a unified research method for ultradiscrete integrable systems
| Project/Area Number |
24540204
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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 | The University of Tokyo |
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Principal Investigator |
WILLOX Ralph 東京大学, 数理(科)学研究科(研究院), 教授 (20361610)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 可積分系 / 離散可積分系 / 超離散可積分系 / セルオートマトン / ソリトン現象 |
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| Outline of Final Research Achievements |
Studying so-called "ultradiscrete integrable systems" - which are special discrete dynamical systems in which all the variables, including the dependent ones, only take discrete values - I discovered an entirely new method for solving such systems.
In particular, this enabled me to solve the so-called "ultradiscrete sine-Gordon equation" for which no explicit solutions are known, over the set of the integers. It also proved possible to attach a combinatorial interpretation to data that appear in the initial value problem for the ultradiscrete version of the famous KdV equation.
Furthermore, concerning integrable systems in the stage before they are turned into ultradiscrete systems, I developed a novel method for constructing higher-dimensional discrete integrable systems and I proposed a novel criterion for deciding on the integrability of lower dimensional discrete dynamical systems.
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Report
(4 results)
Research Products
(15 results)
