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WKB Analysis and Stokes Geometry of Differential Equations

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Book cover Analytic, Algebraic and Geometric Aspects of Differential Equations

Part of the book series: Trends in Mathematics ((TM))

Abstract

In this article we survey the fundamental theory of the exact WKB analysis, that is, the WKB analysis based on the Borel resummation method. Starting with the exact WKB analysis for second order linear ordinary differential equations, we explain its application to the computation of monodromy groups of Fuchsian equations and its generalization to higher order equations. Some recent developments of the theory such as the exact WKB analysis for completely integrable systems are also briefly discussed.

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Acknowledgements

The author would like to thank Dr. Shinji Sasaki for his kind help in preparing some figures contained in this article. This research is supported by JSPS KAKENHI Grant No. 26287015 and No. 24340026.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Doshisha University, Kyotanabe, Kyoto, 610-0321, Japan

    Yoshitsugu Takei

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  1. Yoshitsugu Takei
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Correspondence to Yoshitsugu Takei .

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Editors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

    Galina Filipuk

  2. Kumamoto University, Kumamoto, Japan

    Yoshishige Haraoka

  3. Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszynski University, Warsaw, Poland

    Sławomir Michalik

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Takei, Y. (2017). WKB Analysis and Stokes Geometry of Differential Equations. In: Filipuk, G., Haraoka, Y., Michalik, S. (eds) Analytic, Algebraic and Geometric Aspects of Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-52842-7_5

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