The use of Borel-summation in the establishment of non-existence of certain travelling-wave solutions of the Kuramoto-Sivashinsky equation
type: Item
instance of: scholarly article
title: The use of Borel-summation in the establishment of non-existence of certain travelling-wave solutions of the Kuramoto-Sivashinsky equation
zbMATH Open document ID: 0785.34037
DOI: 10.1016/0165-2125(92)90055-7
published in: Wave Motion
publication date: 1993-04-01T00:00:00Z
review text: A method to prove the nonexistence of regular shocks for the Kuramoto- Sivashinsky equation \(\varepsilon^ 2u_{qqq} +(1-4 \varepsilon^ 2)u_ q=1-u^ 2\), \(u=u(q)\), when \(\varepsilon\) is sufficiently small, is developed. In a joint paper with \textit{A. P. Hooper} [Physica D 50, 231-238 (1991)] the author shows that instead of the condition \(u_{qq}=0\) at \(q=0\) we have \(u_{qq} (0) \sim -2 \gamma \varepsilon^{-4} \exp (-\pi (2 \varepsilon)^{-1})\), \(\varepsilon\to 0\). In this note an alternative procedure for finding \(\gamma\) is described. Using the Borel summation method the value of \(\gamma\) is calculated: \(\gamma=1,9652\dots\).
reviewed by: Y.P.Mishev
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 34B30
zbMATH DE Number: 147211
zbMATH Keywords: nonexistence of regular shocks
zbMATH Keywords: Kuramoto-Sivashinsky equation
author: R. H. J. Grimshaw
MaRDI profile type: Publication
full work available at URL: 0165-2125(92)90055-7
OpenAlex ID: W2056235632
cites work: The non-existence of a certain class of travelling wave solutions of the Kuramoto-Sivashinsky equation
cites work: Asymptotics beyond All Orders in a Model of Crystal Growth
cites work: Structural stability of the Korteweg-de Vries solitons under a singular perturbation
cites work: Q3207312
description: scientific article; zbMATH DE number 147211