IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-4-431-73240-2_5.html
   My bibliography  Save this book chapter

Virtual turning points — A gift of microlocal analysis to the exact WKB analysis

In: Algebraic Analysis of Differential Equations

Author

Listed:
  • Takashi Aoki

    (Kinki University, School of Science and Engineering)

  • Naofumi Honda

    (Hokkaido University, Department of Mathematics, Graduate School of Science)

  • Takahiro Kawai

    (Kyoto University, Research Institute for Mathematical Sciences)

  • Tatsuya Koike

    (Kyoto University, Department of Mathematics, Graduate School of Science)

  • Yukihiro Nishikawa

    (Hitachi Ltd.)

  • Shunsuke Sasaki

    (Mitsubishi UFJ Securities Co. Ltd.)

  • Akira Shudo

    (Tokyo Metropolitan University, Department of Physics, Graduate School of Science)

  • Yoshitsugu Takei

    (Kyoto University, Research Institute for Mathematical Sciences)

Abstract

Several aspects of the notion of virtual turning points are discussed; its background, its relevance to the bifurcation phenomena of a Stokes curve, its importance in the analysis of the Noumi-Yamada system (a particular higher order Painlevé equation) and a concrete recipe for locating them. Examples given here make it manifest that virtual turning points are indispensable in WKB analysis of higher order linear ordinary differential equations with a large parameter.

Suggested Citation

  • Takashi Aoki & Naofumi Honda & Takahiro Kawai & Tatsuya Koike & Yukihiro Nishikawa & Shunsuke Sasaki & Akira Shudo & Yoshitsugu Takei, 2008. "Virtual turning points — A gift of microlocal analysis to the exact WKB analysis," Springer Books, in: Takashi Aoki & Hideyuki Majima & Yoshitsugu Takei & Nobuyuki Tose (ed.), Algebraic Analysis of Differential Equations, pages 29-43, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-73240-2_5
    DOI: 10.1007/978-4-431-73240-2_5
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-4-431-73240-2_5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.