| Project/Area Number |
14340042
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
KAWAI Takahiro KYOTO UNIVERSITY, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (20027379)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
TAKEI Yoshitsugu KYOTO UNIVERSITY, Research Institute for Mathematical Sciences, Associate Professor, 数理解析研究所, 助教授 (00212019)
AOKI Takashi Kinki University, School of Science and Engineering, Professor, 理工学部, 教授 (80159285)
KOIKE Tatsuya KYOTO UNIVERSITY, Graduate School of Sciences, Assistant Professor, 大学院理学研究科, 助手 (80324599)
吉野 正史 広島大学, 理学研究科, 教授 (00145658)
|
|---|
| Project Period (FY) |
2002 – 2004
|
| Project Status |
Completed (Fiscal Year 2004)
|
| Budget Amount *help |
¥6,600,000 (Direct Cost: ¥6,600,000)
Fiscal Year 2004: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2003: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2002: ¥2,900,000 (Direct Cost: ¥2,900,000)
|
|---|
| Keywords | exact WKB analysis / a higher order Painleve equation / The Toulouse Project / a microdifferential operator of WKB type / a virtual turning point / the exact steepest descent method / singular perturbation theory / algebraic analysis / 高階パンルヴェ方式 / Toulouse Project / 野海・山田系 / Lax対 / ストークス曲線 / ストークス図形 / WKB型擬微分作用素 / 高階バンルヴェ方程式 / ストーク図形 / 西川現象 / 0-パラメタ解 / 第1種の変わり点 / 第2種の変わり点 / 無限個の相 / WKB型微分作用素 / Stokes図形 / 超局所微分作用素 / Landau-Zener型 / 陪特性グラフ |
|---|
| Research Abstract |
1.A structure theorem for solutions of a higher order Painleve equation.
Kawai and Takei(Proc. Japan Acad., 80A(2004) have succeeded in transforming any 0-parameter solution of any member of the Painleve hierarchy(P_J)(J=I, II-1,II-2) to that of the classical Painleve-I equation near its turning point of the first kind. This success has made us convinced that the exact WKB analysis should be efficient in studying the structure of higher order Painleve equations, leading to our Announcement of the Toulouse Project(RIMS Kokyuroku 1397(2004)).
2.Proposal of the exact steepest descent method, and its applications. We have confirmed the efficiency of the newly proposed method, the exact steepest descent method, in the situation where the traditional WKB method cannot be applied. (Aoki-Kawai-Takei : Adv. Studies in Pure Math., 42(2004) ; Aoki-Koike-Takei, and Koike-Takei : in Microlocal Analysis and Complex Fourier Analysis, World Scientific,2002).
3.Motivated by a basic integral equation in the plasma physics, we have developed the exact WKB analysis for (micro)differential operators of WKB type. (Aoki-Kawai-Koike-Takei : Adv.in Math.,181(2004),Ann. Inst. Fourier,54 (2004), Contemporary Math.,373(2005), AMS).
4.We have made it manifest that the notion of virtual turning points introduced by Aoki-Kawai-Takei is an indispensable one in the WKB analysis of higher order differential equations. (Kawai-Koike-Nishikawa-Takei : Asterisque,297(2004), Soc. Math. France ; Aoki-Kawai-Sasaki-Shudo-Takei : J.Phys., A38(2005)).
|
