“This monograph provides an introduction to the theory of virtual turning points and its applications as well as a historical view of the theory. … The monograph is written for researchers and students working in mathematical sciences.” (Takashi Aoki, zbMATH 1354.34003, 2017)
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.
