Virtual Turning Points

Nonfiction, Science & Nature, Mathematics, Differential Equations, Science, Physics, Mathematical Physics
Cover of the book Virtual Turning Points by Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei, Springer Japan
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Author: Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei ISBN: 9784431557029
Publisher: Springer Japan Publication: July 7, 2015
Imprint: Springer Language: English
Author: Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei
ISBN: 9784431557029
Publisher: Springer Japan
Publication: July 7, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

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