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Virtual turning points

Honda, Naofumi.

Virtual turning points

Record Type:	Electronic resources : Monograph/item
Title/Author:	Virtual turning pointsby Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei.
Author:	Honda, Naofumi.
other author:	Kawai, Takahiro.
Published:	Tokyo :Springer Japan :2015.
Description:	xii, 126 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Stokes equations.
Online resource:	http://dx.doi.org/10.1007/978-4-431-55702-9
ISBN:	9784431557029 (electronic bk.)

Virtual turning points
Honda, Naofumi.

Virtual turning points[electronic resource] /by Naofumi Honda, Takahiro Kawai, Yoshitsugu Takei. - Tokyo :Springer Japan :2015. - xii, 126 p. :ill. (some col.), digital ;24 cm. - SpringerBriefs in mathematical physics,v.42197-1757 ;. - SpringerBriefs in mathematical physics ;v.1..

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.

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 Painleve 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.

ISBN: 9784431557029 (electronic bk.)

Standard No.: 10.1007/978-4-431-55702-9doiSubjects--Topical Terms:

728102
Stokes equations.

LC Class. No.: QA927

Dewey Class. No.: 518.64

Virtual turning points
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520 $a 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 Painleve 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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