| Project/Area Number |
26400128
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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 |
Basic analysis
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| Research Institution | Kwansei Gakuin University |
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Principal Investigator |
Kotani Shinichi 関西学院大学, 特定プロジェクト研究センター, 客員研究員 (10025463)
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| Co-Investigator(Kenkyū-buntansha) |
千代延 大造 関西学院大学, 理工学部, 教授 (50197638)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2016: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
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| Keywords | シュレーデインガー作用素 / KdV方程式 / スペクトル / 力学系 / Toeplitz作用素 / Weyl関数 / シュレーディンガー作用素 / 佐藤理論 / Herglotz関数 / Darboux変換 |
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| Outline of Final Research Achievements |
Since the discovery of the deep connection between the KdＶ equation describing the dynamics of shallow water wave and the spectrum (eigenvalue) of 1d Schroedinger operator, the KdV equation has been studied in algebra, analysis and geometry as a typical completely integrable system. In this program we take a look of algebraic Sato's theory from the point of spectral theory of Schroedinger operators, and try to construct a solution to the KdV equation starting from a general initial data. To this end we could succeed to obtain an expression of the tau-function by the Weyl function for 1d Schroedinger operator. The tau-function is the key object in Sato's theory. This expression made it possible to give a general solution to the KdV equation.
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