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＜E-Book＞
Virtual Turning Points / by Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei
(SpringerBriefs in Mathematical Physics. ISSN:21971765 ; 4)

Edition	1st ed. 2015.
Publisher	(Tokyo : Springer Japan : Imprint: Springer)
Year	2015
Language	English
Size	XII, 126 p. 47 illus., 6 illus. in color : online resource
Authors	*Honda, Naofumi author Kawai, Takahiro author Takei, Yoshitsugu author SpringerLink (Online service)
Subjects	LCSH:Mathematical physics LCSH:Differential equations LCSH:Quantum physics FREE:Mathematical Physics FREE:Differential Equations FREE:Quantum Physics
Notes	1. Definition and basic properties of virtual turning Points -- 2. Application to the Noumi-Yamada system with a large Parameter -- 3. Exact WKB analysis of non-adiabatic transition problems for 3-levels -- A. Integral representation of solutions and the Borel resummed WKBsolutions 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 HTTP:URL=https://doi.org/10.1007/978-4-431-55702-9

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