Click Here to Download: https://ouo.io/TIm84j Virtual Turning Points By: Naofumi Honda; Takahiro Kawai; Yoshitsugu Takei Publisher: Springer Print ISBN: 9784431557012, 4431557016 eText ISBN: 9784431557029, 4431557024 Copyright year: 2015 Format: PDF Available from $ 54.99 USD SKU 9784431557029 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.
