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Virtual Turning Points

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 4)

DOI: 10.1007/978-4-431-55702-9

ISBN: 978-4-431-55701-2

Publisher: Springer Japan - Springer Journals

Jul 8, 2015

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Chapter 1Definition and Basic Properties of Virtual Turning Points

Honda, Naofumi; Kawai, Takahiro; Takei, Yoshitsugu

Pages: 1 –49

[As we mentioned in Preface, global asymptotic analysis of higher order differential equations was thought impossible to construct in 1980s among specialists in asymptotic analysis. In hindsight we find it reasonable, because neither new Stokes curves nor virtual turning points were not in their...
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Chapter 2Application to the Noumi-Yamada System with a Large Parameter

Honda, Naofumi; Kawai, Takahiro; Takei, Yoshitsugu

Pages: 51 –77

[It is known that a traditional Painlevé equation (of the variable t) is obtained by the compatibility condition of a system of second order linear differential equations of the variables x and t. Here, when we focus upon the underlying linear system, the latter variable t is often called a...
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Chapter 3Exact WKB Analysis of Non-adiabatic Transition Problems for 3-Levels

Honda, Naofumi; Kawai, Takahiro; Takei, Yoshitsugu

Pages: 79 –110

[As we have observed so far, virtual turning points and (new) Stokes curves emanating from them play a crucially important role in discussing the Stokes geometry of a higher order ordinary differential equation and/or a system of ordinary differential equations of size greater than two. Once all...

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