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Virtual Turning Points by Naofumi Honda
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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.

Springer Japan; July 2015
133 pages; ISBN 9784431557029
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Title: Virtual Turning Points
Author: Naofumi Honda; Takahiro Kawai; Yoshitsugu Takei
 
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ISBNs
9784431557012
9784431557029