Nonlinear Stokes problems of the Painleve equation

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400113
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Osaka University
• Principal Investigator: Ohyama Yousuke 大阪大学, 情報科学研究科, 准教授 (10221839)
• Co-Investigator(Renkei-kenkyūsha): Watanabe Humihiko 北見工業大学, 工学部, 准教授 (20274433) ; Suzuki Takao 近畿大学, 理工学部, 准教授 (60527208)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: パンルヴェ方程式 / q-差分方程式 / 接続問題

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.

Free Research Field

古典解析学