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December 2004 On the Complex WKB Analysis for a Second Order Linear O.D.E. with a Many-Segment Characteristic Polygon
Minoru NAKANO
Tokyo J. Math. 27(2): 411-442 (December 2004). DOI: 10.3836/tjm/1244208399

Abstract

Asymptotics of ODE appearing in the turning point problems can be characterized literally by its characteristic polygon. The Airy equation has a one-segment characteristic polygon. Fedoryuk ([4]), Nakano ([8], [12]), Nakano et al. ([13]), and Roos ([17], [18]) studied ODE's with a several-segement one. The more segments, the more complicated asymptotics. Here, we study an ODE with a many-segment one. Firstly, the ODE is reduced to the simpler ODE's in some subdomains, and then the reduced ODE's have the WKB solutions as their asymptotic solutions. Secondly, two sets of the WKB solutions in the neighboring subdomains are related by a matching matrix. In our analysis the stretching-matching method is applied and the Stokes curves play an important role. How to get the Stokes curve configuration for the reduced ODE's is analyzed precisely.

Citation

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Minoru NAKANO. "On the Complex WKB Analysis for a Second Order Linear O.D.E. with a Many-Segment Characteristic Polygon." Tokyo J. Math. 27 (2) 411 - 442, December 2004. https://doi.org/10.3836/tjm/1244208399

Information

Published: December 2004
First available in Project Euclid: 5 June 2009

zbMATH: 1082.34081
MathSciNet: MR2107593
Digital Object Identifier: 10.3836/tjm/1244208399

Rights: Copyright © 2004 Publication Committee for the Tokyo Journal of Mathematics

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Vol.27 • No. 2 • December 2004
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