An example of Newton's method for an equation in Gevrey series
type: Item
instance of: scholarly article
title: An example of Newton's method for an equation in Gevrey series
zbMATH Open document ID: 1309.34147
author: Alexander Getmanenko
published in: Journal of Differential Equations
publication date: 2014-10-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/1304.6621
review text: A generalization of the paper of \textit{T. Aoki} et al. [Adv. Stud. Pure Math. 54, 19--94 (2009; Zbl 1175.34112)], the author discusses the reduction problem for one-dimensional Schrödinger equations near a multiple turning point. Constructing a functional analytic framework based essentially on the idea of the use of Banach scales for the purpose of treating factorially divergent Gevrey series (with respect to the Planck constant) and employing Newton's method of tangents in this framework, he shows that near a multiple turning point a one-dimensional Schrödinger equation can be transformed to a canonical form by a change of independent variable, which is analytic near a point in question and factorially divergent with respect to the Planck constant.
reviewed by: Yoshitsugu Takei
Mathematics Subject Classification ID: 34M60
Mathematics Subject Classification ID: 34M25
zbMATH DE Number: 6359825
zbMATH Keywords: anharmonic oscillator
zbMATH Keywords: complex WKB
MaRDI profile type: Publication
OpenAlex ID: W2964289419
arXiv ID: 1304.6621
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DOI: 10.1016/J.JDE.2014.09.002
description: scientific article; zbMATH DE number 6359825