| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Outline of Final Research Achievements |
We study a q-analogue of the Painleve equation, which is a difference equation. The main subject is a study of local behavior of generic solutions of q-Painleve equations around a fixed singular point. In case of nonlinear q-difference equation, it is difficult to express local behavior of solutions. We solve a connection problem of some linear q-difference equations with irregular singular points at first. Then we express local behavior of generic solutions of q-Painleve equations around the origin in terms of connection coefficients of the linear q-difference equation. In cases of degenerated q-Painleve equations, the corresponding linear equation has an irregular singular point. Since some local solutions are represented by divergent series, the Stokes phenomenon appears. We decided the Stokes coefficients by means of connection coefficients of q-hypergeometric equations.
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