Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity
type: Item
instance of: scholarly article
title: Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity
zbMATH Open document ID: 1073.34044
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2004-11-23T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78621
review text: The author studies the fourth-order nonlinear differential equation \[ u^{(\text{IV})}-g(u)u''-g'(u)(u')^2/2+f'(u)=0, \] where \(f\) is a symmetric double-well potential with bottoms at \(\pm 1\) and \(g\) is an even function. Such equations determine stationary solutions for some classes of PDEs (for example, for the extended Fisher-Kolmogorov equation). Conditions are given under which there exist kinks (heteroclinic solutions connecting \(-1\) and \(1\)) with arbitrarily many passages from \(-1\) to \(1\). Pulses (homoclinic solutions) are considered, too.
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 2117897
zbMATH Keywords: Multitransition heteroclinics and homoclinics
zbMATH Keywords: Swift-Hohenberg equation
zbMATH Keywords: Minimization
zbMATH Keywords: Saddle-focus equilibrium
author: Denis Bonheure
reviewed by: Sergei Yu. Pilyugin
MaRDI profile type: Publication
OpenAlex ID: W2145255507
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DOI: 10.1016/J.ANIHPC.2003.03.001
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description: scientific article; zbMATH DE number 2117897