Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 4)
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Table of contents (3 chapters)
Keywords
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.
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Bibliographic Information
Book Title: Virtual Turning Points
Authors: Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei
Series Title: SpringerBriefs in Mathematical Physics
DOI: https://doi.org/10.1007/978-4-431-55702-9
Publisher: Springer Tokyo
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2015
Softcover ISBN: 978-4-431-55701-2Published: 21 July 2015
eBook ISBN: 978-4-431-55702-9Published: 07 July 2015
Series ISSN: 2197-1757
Series E-ISSN: 2197-1765
Edition Number: 1
Number of Pages: XII, 126
Number of Illustrations: 41 b/w illustrations, 6 illustrations in colour
Topics: Mathematical Physics, Ordinary Differential Equations, Quantum Physics
Industry Sectors: IT & Software