Algebraic Analysis of Singular Perturbation Theory (IWANAMI SERIES IN MODERN MATHEMATICS: TRANSLATIONS OF MATHEMATICAL MONOGRAPHS)

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. 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 Painleve Functions. The Volume Is Suitable For Graduate Students And Researchers Interested In Differential Equations And Special Functions.--book Jacket. Ch. 1. Borel Resummation -- Ch. 2. Wkb Analysis Of Schrodinger Equations -- Ch. 3. Applications Of Wkb Analysis Of Global Problems -- Ch. 4. Wkb Analysis Of The Painleve Transcendents. Takahiro Kawai, Yoshitsugu Takei ; Translated By Goro Kato. Includes Bibliographical References (p. 125-128) And Index. 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. Describes the WKB (Wentzel-Kramers-Brillouin) method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painleve functions. This title is suitable for graduate students and researchers interested in differential equations and special functions.