Detecting integrability of discrete equations on multi-dimensional lattices
| Project/Area Number |
16H06711
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Mase Takafumi 東京大学, 大学院数理科学研究科, 特任助教 (80780105)
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| Project Period (FY) |
2016-08-26 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥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 / 代数的エントロピー / 応用数学 / 特異点閉じ込め / 可積分性判定 |
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| Outline of Final Research Achievements |
We studied the integrability of discrete equations on multi-dimensional lattices, by means of cancellation of factors. First, we extended the so-called coprimeness condition. As a result, it has become possible to apply the coprimeness condition to more equations than before. We also showed that the nonlinear form of an extended version of the discrete Toda equation possesses this property. Moreover, in the case of equations on one-dimensional lattices, we developed a method to verify the integrability only by means of singularity confinement. Using the theory of algebraic surfaces, we revealed the meaning of our method in the case of second-order mappings.
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Report
(3 results)
Research Products
(10 results)
