Study on the structure of solutions of Matrix Painleve Systems

Research Project

Project/Area Number	19540219
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Global analysis
Research Institution	Nagasaki University
Principal Investigator	MURATA Yoshihiro Nagasaki University, 経済学部, 教授 (60212255)
Project Period (FY)	2007 – 2009
Project Status	Completed (Fiscal Year 2009)
Budget Amount *help	¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000) Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000) Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords	可積分系 / パンルベ方程式 / 岡本変換 / ヤンミルズ方程式 / 行列型パンルベ方程式 / 変換群
Research Abstract	Investigating transformations of solutions (Backlund transformations) of Matrix Painleve Systems reduced from Anti-Self-Dual Yang-Mills Equations under symmetric conditions, we have shown that some transformations of solutions of Painlve equations (Okamoto transformations) are obtained from conformal transformations and Cauge transformations on spice-time.