2012 Fiscal Year Final Research Report
Theory of integrable hierarchies and its application to mathematical physics
| Project/Area Number |
22540186
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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 |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
SASAKI Ryu 京都大学, 基礎物理学研究所, 准教授 (20154007)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 代数解析 |
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| Research Abstract |
Integrable hierarchies are a class of classical integrable system. Typical examples are the KP hierarchy, the Toda hierarchy and multi-component versions thereof. This research is focussed on both theoretical aspects and applications to mathematical physics. All materials play an important role in recent progress of mathematical physics. As regards the theoretical aspect, we have obtained some results on the Toda hierarchy, the dispersionless Toda hierarchy and integrable hierarchies of the B and D types. Subjects of applications to mathematical physics range over statistical mechanics, gauge theories, string theories and related mathematical issues. Solvable models in discrete quantum mechanics are also studied in the context of orthogonal polynomials.
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