A shooting method for the Swift-Hohenberg equation.
type: Item
instance of: scholarly article
title: A shooting method for the Swift-Hohenberg equation.
zbMATH Open document ID: 1088.34521
author: Youshan Tao
author: Jizhou Zhang
published in: Applied Mathematics. Series B (English Edition)
publication date: 2002-01-01T00:00:00Z
review text: The authors consider the differential equation \[ u^{(4)}+ 2u''+ (1- k)u+ u^3= 0.\tag{\(*\)} \] They prove that for \(0< k< 1\), equation \((*)\) has a periodic solution with the same energy as the solution \(u= 0\), and that for \(1< k<{3\over 2}\), equation \((*)\) has a periodic solution with the same energy as the solutions \(u=\pm \sqrt{k-1}\). The proof is based on the shooting technique and on the fact that \((*)\) has a first integral.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 1877144
zbMATH Keywords: periodic solution
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: s11766-996-0003-6
OpenAlex ID: W2057204617
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DOI: 10.1007/S11766-996-0003-6
description: scientific article; zbMATH DE number 1877144