1998 Fiscal Year Final Research Report Summary
Theory of singular perturbations
| Project/Area Number |
08454029
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
KAWAI Takahiro KYOTO UNIVERSITY,Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (20027379)
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| Co-Investigator(Kenkyū-buntansha) |
OJIMA Izumi KYOTO UNIVERSITY,Research Institute for Mathematical Sciences, Associate Profess, 数理解析研究所, 助教授 (60150322)
MOCHIZUKI Shinichi KYOTO UNIVERSITY,Research Institute for Mathematical Sciences, Associate Profess, 数理解析研究所, 助教授 (10243106)
MUROTA Kazuo KYOTO UNIVERSITY,Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (50134466)
OKAMOTO Hisashi KYOTO UNIVERSITY,Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (40143359)
TAKEI Yoshitsugu KYOTO UNIVERSITY,Research Institute for Mathematical Sciences, Associate Profess, 数理解析研究所, 助教授 (00212019)
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| Project Period (FY) |
1996 – 1998
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| Keywords | Exact WKB analysis / Borel resummation / monodromy groups / Painleve transcendents / multiple-scale / Schrodinger equations / Stokes curves / deformation (of differential equations) |
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| Research Abstract |
(1) Exact WKB analysis, i.e., WKB analysis based on the Borel summation has enabled us to describe the monodromy group for second order Fuchsian equations in terms of period integrals of Borel resummed WKB solutions. (Kawai-Takei, Algebraic Analysis of Singular Perturbations, Chap. 3, Iwanami (in Japanese)).
(2) 2-parameter formal solutions of Painleve equations with a large parameter are constructed by multiple-scale analysis, and then they are shown to be formally and locally reduced to some appropriate 2-parameter solution of the Painleve equation, type I.(Aoki-Kawai-Takei, in "Structure of Solutions of Differential Equations", World Scientific and Kawai and Takei, Adv. in Math., 134)
(3) Singular-perturbative reduction of a Hamiltonian system to the Birkhoff normal form, which may be used as a more transparent substitute of multiple-scale analysis in constructing 2-parameter formal solutions of Painleve equations. (Takei, Publ. RIMS, 34)
(4) A trial of exact WKB analysis for higher order ordinary differential equations with a large parameter through the presentation of Ansatz concerning their Stokes geometry. (Aoki-Kawai-Takei, Asian J.Math. 2)
(5) Asymptotic analysis of natural boundaries of solutions of non-linear differential equations of higher order (such as the Jacobi equation).
(6) Structure theory for non-linear equations other than Painleve equations.
Our study of items (4), (5) and (6) still remain on a preliminary stage.
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Research Products
(15 results)
