TY  - BOOK
AU  - Honda,Naofumi
AU  - Kawai,Takahiro
AU  - Takei,Yoshitsugu
ED  - SpringerLink (Online service)
TI  - Virtual Turning Points
T2  - SpringerBriefs in Mathematical Physics,
SN  - 9784431557029
AV  - QA401-425 
U1  - 530.15 23
PY  - 2015///
CY  - Tokyo
PB  - Springer Japan, Imprint: Springer
KW  - mathematics
KW  - Differential Equations
KW  - Mathematical physics
KW  - Quantum Physics
KW  - Mathematics
KW  - Mathematical Physics
KW  - Ordinary Differential Equations
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-4-431-55702-9
ER  -