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SpringerBriefs in Mathematical Physics

Virtual Turning Points

Authors: Honda, Naofumi, Kawai, Takahiro, Takei, Yoshitsugu

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  • Is the first book that expounds a virtual turning point, a new and important notion in WKB analysis
  • Contains essential know-how in its concrete treatment of the theory of virtual turning points, written by the founders of that theory
  • Establishes an important bridge between pure mathematics and applied mathematics
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  • ISBN 978-4-431-55702-9
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About this book

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.

Reviews

“This monograph provides an introduction to the theory of virtual turning points and its applications as well as a historical view of the theory. … The monograph is written for researchers and students working in mathematical sciences.” (Takashi Aoki, zbMATH 1354.34003, 2017)


Table of contents (3 chapters)

Table of contents (3 chapters)
  • Definition and Basic Properties of Virtual Turning Points

    Pages 1-49

    Honda, Naofumi (et al.)

  • Application to the Noumi-Yamada System with a Large Parameter

    Pages 51-77

    Honda, Naofumi (et al.)

  • Exact WKB Analysis of Non-adiabatic Transition Problems for 3-Levels

    Pages 79-110

    Honda, Naofumi (et al.)

Buy this book

eBook $39.99
price for Mexico
  • ISBN 978-4-431-55702-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for Mexico
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Bibliographic Information

Bibliographic Information
Book Title
Virtual Turning Points
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
4
Copyright
2015
Publisher
Springer Japan
Copyright Holder
The Author(s)
eBook ISBN
978-4-431-55702-9
DOI
10.1007/978-4-431-55702-9
Softcover ISBN
978-4-431-55701-2
Series ISSN
2197-1757
Edition Number
1
Number of Pages
XII, 126
Number of Illustrations
41 b/w illustrations, 6 illustrations in colour
Topics

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