Virtual Turning Points
Seiten
2015
|
1st ed. 2015
Springer Verlag, Japan
978-4-431-55701-2 (ISBN)
Springer Verlag, Japan
978-4-431-55701-2 (ISBN)
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.
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.
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.
| Reihe/Serie | SpringerBriefs in Mathematical Physics ; 4 |
|---|---|
| Zusatzinfo | 6 Illustrations, color; 41 Illustrations, black and white; XII, 126 p. 47 illus., 6 illus. in color. |
| Verlagsort | Tokyo |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| Schlagworte | a bicharacteristic curve • a new Stokes curve • a virtual turning point • Borel transformation • exact WKB analysis |
| ISBN-10 | 4-431-55701-6 / 4431557016 |
| ISBN-13 | 978-4-431-55701-2 / 9784431557012 |
| Zustand | Neuware |
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