Virtual Turning Points

  • Naofumi Honda
  • Takahiro Kawai
  • Yoshitsugu Takei

Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 4)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei
    Pages 1-49
  3. Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei
    Pages 51-77
  4. Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei
    Pages 79-110
  5. Back Matter
    Pages 111-126

About this book

Introduction

The discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi–Yamada type and to the analysis of non-adiabatic transition probability problems in three levels.

As M.V. Fedoryuk once lamented, global asymptotic analysis of higher order differential equations had been thought to be impossible to construct. In 1982, however, H.L. Berk, W.M. Nevins, and K.V. Roberts published a remarkable paper in the Journal of Mathematical Physics indicating that the traditional Stokes geometry cannot globally describe the Stokes phenomena of solutions of higher order equations; a new Stokes curve is necessary.

Keywords

Borel transformation a bicharacteristic curve a new Stokes curve a virtual turning point exact WKB analysis

Authors and affiliations

  • Naofumi Honda
    • 1
  • Takahiro Kawai
    • 2
  • Yoshitsugu Takei
    • 3
  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan
  2. 2.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  3. 3.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-4-431-55702-9
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Tokyo
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-4-431-55701-2
  • Online ISBN 978-4-431-55702-9
  • Series Print ISSN 2197-1757
  • Series Online ISSN 2197-1765
  • About this book