| Budget Amount *help |
¥8,710,000 (Direct Cost: ¥6,700,000、Indirect Cost: ¥2,010,000)
Fiscal Year 2023: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2022: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2021: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
To establish the exact WKB analysis for systems of differential equations including nonlinear equations and difference equations we study Painleve equations and hypergeometric systems from the viewpoint of the exact WKB analysis. Consequently the problem of analytic interpretation of instanton solutions for Riccati equations, which can be considered as prototype of Painleve equations, is solved and further the following new results are obtained: the structure of Stokes geometry of the difference equation for Bessel functions is clarified, Voros coefficients of Weber functions are determined and integral representations of Gauss' hypergeometric functions are derived by utilizing a system of differential-difference equations. It is also shown that WKB-type formal solutions of initial value problems for time-dependent Schrodinger equations can be analytically interpreted in several simple cases through stochastic differential equations.
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