2012 Fiscal Year Final Research Report
Analysis for integrable cellular automata by ultradiscretization method and its applications to non-integrable systems
| Project/Area Number |
21760063
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Engineering fundamentals
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| Research Institution | Hosei University (2012)
Aoyama Gakuin University (2009-2011) |
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Principal Investigator |
ISOJIMA Shin 法政大学, 理工学部, 准教授 (90422394)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 数理物理 / 可積分系 / セルオートマトン / 超離散化 |
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| Research Abstract |
We proposed a procedure `ultradiscretization with parityvariables’, which is an extended version of usual ultradiscretization method. By meansof this procedure, we obtained various results on integrable cellular automata, forexample, construction of an ultradiscrete analog of the q-Painleve II equation and a classof its special solutions. We studied oscillatory solutions of ultradiscrete systems,derivation of soliton solutions to the Box and Ball system based on an algebro-geometricmethod and so on by usual ultradiscretization method. We also investigated anultradiscrete analog of the optimal velocity model and Kalman filter for apiecewise-linear system, which are non-integrable systems.
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