Shimomura, Shun

写真a

Affiliation

Faculty of Science and Technology ( Mita )

Position

Professor Emeritus

External Links
Scopus Paper Info  
Paper Count: 62 Citation Count: 364 h-index: 11

Click to view the Scopus page. The data was downloaded from Scopus API in May 10, 2026, via http://api.elsevier.com and http://www.scopus.com .

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Career 【 Display / hide 】

  • 1979.04
    -
    1982.01

    科学技術庁航空宇宙技術研究所総理府 ,技官

  • 1982.02
    -
    1988.03

    神戸大学（大学院自然科学研究科） ,助手

  • 1988.04
    -
    1996.03

    慶應義塾大学（理工学部数理学科） ,専任講師

  • 1990.04
    -
    1991.03

    東海大学（微積分Ａ） ,非常勤講師

  • 1991.10
    -
    1992.03

    東海大学（微積分） ,非常勤講師

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Academic Background 【 Display / hide 】

  • 1976.03

    The University of Tokyo, Faculty of Science, 数学科

    University, Graduated

  • 1978.03

    The University of Tokyo, Graduate School, Division of Science, 数学専攻

    Graduate School, Completed, Master's course

  • 1979.03

    The University of Tokyo, Graduate School, Division of Science, 数学専攻

    Graduate School, Withdrawal before completion, Doctoral course

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Academic Degrees 【 Display / hide 】

  • 理学　, The University of Tokyo, 1984.04

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Books 【 Display / hide 】

  • Nevanlinna 理論の微分方程式への応用

    SHIMOMURA SHUN, 神戸大学理学部数学教室, 2003

  • Painleve Differential Equations in the Complex Plane

    V. Gromak; SHIMOMURA SHUN; I. Laine, Walter de Gruyter, Berlin, 2002

  • From Gauss to Painleve, A Modern Theory of Special Functions

    K.Iwasaki,H.Kimura, SHIMOMURA SHUN, Y.Yoshida, vieweg, 1991.04

    　View Summary

    超幾何方程式、モノドロミー保存変形Painleve方程式について解説した。全347頁。　Studies on nonlinear differential equations

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Papers 【 Display / hide 】

  • Explicit Error Term of the Elliptic Asymptotics for the First Painlevé Transcendents

    Shimomura S.

    Computational Methods and Function Theory  2025

    Research paper (scientific journal), Single Work, Lead author, Corresponding author, Accepted,  ISSN  16179447

    　View Summary

    For the first Painlevé transcendents Kitaev established an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips tending along generic directions near the point at infinity. For this elliptic expression we present an explicit asymptotic formula of the error term, which leads to the error bound of exponent.

    final version

  • Elliptic Asymptotics for the Complete Third Painlevé Transcendents

    Shimomura S.

    Funkcialaj Ekvacioj 68 ( 1 ) 69 - 117 2025

    Single Work, Lead author, Corresponding author, Accepted,  ISSN  05328721

    　View Summary

    For a general solution of the third Painlevé equation of complete type we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Jacobi sn-function in cheese-like strips along generic directions. The expression is derived by using isomonodromy deformation of a linear system governed by the third Painlevé equation of this type. In our calculation of the WKB analysis, the treated Stokes curve ranges on both upper and lower sheets of the two sheeted Riemann surface.

  • TWO ERROR BOUNDS OF THE ELLIPTIC ASYMPTOTICS FOR THE FIFTH PAINLEVÉ TRANSCENDENTS

    Shimomura S.

    Kyushu Journal of Mathematics 78 ( 2 ) 487 - 502 2024

    Single Work, Lead author, Corresponding author, Accepted,  ISSN  13406116

    　View Summary

    For the fifth Painlevé equation it is known that a general solution is represented asymptotically by an elliptic function in cheese-like strips near the point at infinity. We present an explicit asymptotic formula for the error term of this expression, which leads to the error bound as was conjectured. An analogous formula with its bound is obtained for the error term of the correction function associated with the Lagrangian.

    PDF1

  • Boutroux Ansatz for the Degenerate Third Painlevé Transcendents

    Shimomura S.

    Publications of the Research Institute for Mathematical Sciences 60 ( 4 ) 651 - 698 2024

    Research paper (bulletin of university, research institution), Lead author, Corresponding author, Accepted,  ISSN  00345318

    　View Summary

    For a general solution of the degenerate third Painlevé equation we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips along generic directions. The expression is obtained by using isomonodromy deformation of a linear system governed by the degenerate third Painlevé equation.

  • Elliptic asymptotic representation of the fifth Painleve transcendents. Corrected and revised version

    Shun Shimomura

    arXiv:2012.07321, math.CA, math-ph (arXiv:2012.07321, math.CA, math-ph)   2023.12

    Research paper (other academic), Single Work, Lead author, Corresponding author

    　View Summary

    Corrected the errors of the paper published in
    Kyushu Journal of Mathematics Vol.76 no.1 (2022),
    and extensively revised for readability.

    corrected and revised version

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Presentations 【 Display / hide 】

  • Boutroux ansatz for the degenerate third Painlev\'e transcendents

    Shun Shimomura

    [International presentation]  Web-seminar on Painleve Equations and related topics, 

    2025.03
    , 

    Public lecture, seminar, tutorial, course, or other speech

    　View Summary

    Abstract : The degenerate third Painlev\'e equation P3d has quite different
    properties from those of the complete third Painlev\'e equation; for
    example, P3d admits algebraic solutions written by the cube root. For a
    general solution of P3d we show the Boutroux ansatz, that is, present an
    asymptotic elliptic expression near the point at infinity. Applying some
    changes of variables to P3d and to the related isomonodromy linear system,
    we rewrite them in the forms suitable for our purpose, and examine the
    manifold of monodromy data. For this linear system we first solve the
    direct monodromy problem by WKB analysis, and in the next step for given
    monodromy data we find an asymptotic form of the desired solution as
    solution to the inverse monodromy problem, the validity of which is
    guaranteed by Kitaev's justification scheme. Consequently we obtain an
    asymptotic representation in terms of the Weierstrass pe-function in
    cheese-like strips along generic directions. Publ.~RIMS Kyoto Univ. 60
    (2024), arXiv:2207.11495

  • Elliptic asymptotics for Painleve transcendents

    下村 俊

    Tokushima Classical Analysis seminar (徳島大学常三島キャンパス・共通教育棟　部屋K304) , 

    2023.10
    , 

    Public lecture, seminar, tutorial, course, or other speech, 大山陽介 徳島大学大学院社会産業理工学研究部

    　View Summary

    Painleve 方程式 PI, PII の解の無限遠点近くでの漸近的振る舞いは楕円函数により
    表現されることが，1910 年代に Boutroux により見出された.その論文自体は近づき難い
    ものであるが，Boutroux 自身はその本質は把握していたように思われる.
    PI, PII の解の elliptic な漸近表現は 1990 年前後に Joshi と Kruskal が multiscale expansions の
    方法によりもとめた.そしてモノドロミー保存変形を用いた方法で PII の elliptic な漸近表現を
    得たのは Novokshenov が最初であり，その後少し異なったやりかたで Kapaev, Kitaev が
    PI, PII の漸近表現を導いた. また最近の Iwaki の PI に関する研究では topological recursion の
    方法により τ-function のレベルで漸近表現の構成に成功した. この講演で は PV にモノドロミー
    保存変形の方法を用いて elliptic な漸近表現を与える.また時間 が許せば，PIII(D6), PIII(D7) に
    ついての結果，今後の問題などにも言及する.

  • Painlev'e V に関連した Schlesinger 方程式の解について

    下村 俊

    [Domestic presentation]  研究集会「複素領域における微分方程式とその周辺」 (北海道大学理学部５号館（低層棟）３階５－３０１室) , 

    2018.08
    , 

    Oral presentation (invited, special), 木村 弘信（熊本大理） 岩﨑 克則（北大理）

  • Painleve 超越関数の振る舞いについて

    SHIMOMURA SHUN

    [Domestic presentation]  Tokyo Journal of Mathematics 筱田記念号刊行に寄せて (上智大学) , 

    2016.03
    , 

    Oral presentation (invited, special)

  • On certain nonlinear differential equations

    SHIMOMURA SHUN

    [International presentation]  The 12th International Conference on Finite and Infinite Dimensional Complex Analysis and Applications (国際キリスト教大学) , 

    2004.07
    , 

    Oral presentation (invited, special)

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Courses Taught 【 Display / hide 】

  • FUNCTIONAL EQUATIONS 2

    2020

  • FUNCTIONAL EQUATIONS 2

    2019

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Social Activities 【 Display / hide 】

  • Mathematical Review

    1999
    -
    Present

  • Zentralblatt fur Mathematik

    1998.07
    -
    Present
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Memberships in Academic Societies 【 Display / hide 】

  • 日本数学会

    　
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Committee Experiences 【 Display / hide 】

  • 1998.07
    -
    Present

    reviewer, Zentralblatt fur Mathematik

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