Asymptotic analysis on the Painleve equations and monodromy problems

Painleve方程和单调问题的渐近分析

• 批准号: 21540217
• 负责人: OHYAMA Yousuke
• 金额: $ 2.83万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540217/
• 关键词: 可積分系; パンルヴェ方程式; 漸近解析; カルタン幾何; q-パンルヴェ方程式; 超幾何函数; 代数函数; モノドロミ; モノドロミ非保存変形

We study special solutions of the q-Painleve equations. In the case| q|=1, the first and the second q-Painleve equation has convergent solutions around the infinity. If q is a root of unity, they are represented by hypergeometric functions. We gave a coalescent diagram for q-hypergeometric functions and we obtain seven q-difference linear equations. For classical Painleve equations, we are studying convergence of asymptotic expansions. We also studied that monodromy evolving deformations for irregular singular cases.

研究了q-Painleve方程的特解。的情况下|Q| =1时，第一和第二类q-Painleve方程在无穷远处有收敛解.如果q是单位根，则它们由超几何函数表示。给出了q-超几何函数的结合图，得到了七个q-差分线性方程。对于经典的Painleve方程，我们研究渐近展开式的收敛性。研究了非规则奇异情形下的单值演化变形。

项目成果

Particular solutions of q-Painleve equations and q-hypergeometric equations

q-Painleve 方程和 q-超几何方程的特解

• 发表时间: 2011
• 期刊: Proceeding of International Conference" Painleve Equations and Related Topics"
• 作者: P.Baseilhac;T.Kojima;Tatsuo Iguchi;塩路直樹 渡辺宏太郎;H. Sumi;Yousuke Ohyama
• 通讯作者: Yousuke Ohyama

Analytic solutions to the Painleve equations around the origin

原点附近 Painleve 方程的解析解

• 发表时间: 2009
• 作者: E.Messina;Y.Muroya;Y.Nakata;E.Russo;A.Vecchio;Tetsutaro Shibata;塩路直樹;増田哲;Yousuke Ohyama
• 通讯作者: Yousuke Ohyama

Boutroux100 :パンルヴェ方程式の漸近解析

Boutroux100：Painlevé 方程的渐近分析

• 发表时间: 2012
• 作者: Y. Nakata;Y. Enatsu and Y. Muroya;大山陽介
• 通讯作者: 大山陽介

Asymptotics of the Painleve equations and Hukuhara' s theorem

Painleve 方程和 Hukuhara 定理的渐近

• 发表时间: 2011
• 作者: Y. Muroya;Y. Enatsu and Y. Nakata;角大輝;井口達雄;高野恭一;塩路直樹;大山陽介;T.Kojima;M. Kuroda and Y. Muroya;井口達雄;Yoshio Yamada;Yousuke Ohyama
• 通讯作者: Yousuke Ohyama

Asymptotics of the Painleve equations and Hukuhara's theorem

Painleve 方程和 Hukuhara 定理的渐近

• 发表时间: 2011
• 作者: Y. Enatsu;Y. Nakata and Y. Muroya;Yousuke Ohyama
• 通讯作者: Yousuke Ohyama