Algebraic Analysis of Singular Perturbation Theory

by Takahiro Kawai

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 method used 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 Painleve functions. The volume is suitable for graduate students and researchers interested in differential equations and special functions.

129 pages, Paperback

First published January 1, 2006

Reviews

[The Architect]

Standard reference on exact WKB; summarized in arXiv:1401.7094 and arXiv:1409.4641 where it is generalized to compact Riemann surfaces of genus g > 0.