On the WKB method for certain third order ordinary differential equations
type: Item
instance of: scholarly article
title: On the WKB method for certain third order ordinary differential equations
zbMATH Open document ID: 0748.34038
author: Minoru Nakano
author: Masatoshi Namiki
author: Toshihiko Nishimoto
published in: Kodai Mathematical Journal
publication date: 1992-09-26T00:00:00Z
review text: The authors consider the WKB type asymptotic expansions of solutions to third order linear ordinary differential equations of the form \(\varepsilon^ 3y'''+\varepsilon^ 2p_ 1(x)y''+\varepsilon p_ 2(x)y'+p_ 3(x)y=0\), in the whole complex \(x\)-plane. The formal solutions are constructed by the WKB method; an existence theorem is given; questions such as the Stokes curve configuration, existence of admissible domains, the connection rules in the whole complex \(x\)-plane are considered, which had been considered by other authors for second order ordinary differential equations.
Mathematics Subject Classification ID: 34E20
Mathematics Subject Classification ID: 34M99
zbMATH DE Number: 55876
zbMATH Keywords: WKB type asymptotic expansions
zbMATH Keywords: third order linear ordinary differential equations
zbMATH Keywords: WKB method
zbMATH Keywords: Stokes curve configuration
zbMATH Keywords: connection rules
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039466
OpenAlex ID: W1977372462
cites work: New Stokes’ line in WKB theory
cites work: Q5561154
cites work: Q5723358
cites work: General connection formulae for Liouville-Green approximations in the complex plane
cites work: Q3786786
cites work: Q3041568
DOI: 10.2996/KMJ/1138039466
description: scientific article; zbMATH DE number 55876