| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
The aim of this study was to expand the perspective of the "tau function" introduced in the study of integrable systems, and to explore its relationship with various fields in order to expand the world of integrable systems. The following results were obtained: (1) An alternative proof from the viewpoint of "Hirota's direct method" regarding the relationship between the maximum eigenvalue distribution function of the GUE-type ensemble and the Painleve IV equation. (2) Description of "rigged configurations" of sl2 type using soliton automata. (3) Relationship between the lattice KdV equation, lattice Boussinesq equation, and Toda hierarchy. (4) Construction of algebraic-geometric tau functions of the lattice soliton equation.
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