Descript 
1 online resource (xii, 126 pages) : illustrations (some color), digital ; 24 cm 

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computer c rdamedia 

online resource cr rdacarrier 

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Series 
SpringerBriefs in mathematical physics, 21971757 ; volume 4


SpringerBriefs in mathematical physics ; volume 4

Note 
1. Definition and basic properties of virtual turning Points  2. Application to the NoumiYamada system with a large Parameter  3. Exact WKB analysis of nonadiabatic transition problems for 3levels  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 Painleve equations of the NoumiYamada type and to the analysis of nonadiabatic 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 
Host Item 
Springer eBooks

Subject 
Stokes equations


Mathematics


Mathematical Physics


Ordinary Differential Equations


Quantum Physics

Alt Author 
Kawai, Takahiro, author


Takei, Yoshitsugu, author


SpringerLink (Online service)

