Algebraic Analysis of Singular Perturbation Theory
About this Title
Takahiro Kawai, Kyoto University, Kyoto, Japan and Yoshitsugu Takei, Kyoto, Japan. Translated by Goro Kato
Publication: Translations of Mathematical Monographs
Publication Year: 2005; Volume 227
ISBNs: 978-0-8218-3547-0 (print); 978-1-4704-4651-2 (online)
MathSciNet review: MR2182990
MSC: Primary 34-02; Secondary 34E15, 34E20, 34M60
The topic of this book is the study of singular perturbations of ordinary differential equations, i.e., perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter. The main approach used by the authors is the so-called WKB (Wentzel–Kramers–Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painlevé functions. The volume is suitable for graduate students and researchers interested in differential equations and special functions.
Graduate students and research mathematicians interested in differential equations and special functions.
Table of Contents
- Borel resummation
- WKB analysis of Schrödinger equations
- Applications of WKB analysis to global problems
- WKB analysis of the Painlevé transcendants
- Future directions and problems