The Peierls-Nabarro and Benjamin-Ono equations
type: Item
instance of: scholarly article
title: The Peierls-Nabarro and Benjamin-Ono equations
zbMATH Open document ID: 0876.35106
published in: Journal of Functional Analysis
publication date: 1997-11-25T00:00:00Z
review text: An intimate connection between the Peierls-Nabarro equation in crystal-dislocation theory and the travelling-wave form of the Benjamin-Ono equation in hydrodynamics is uncovered. It is used to prove the essential uniqueness of Peierls solution of the Peierls-Nabarro equation and to give, in closed form, all solutions of the analogous periodic problem. The latter problem is shown to be an example of global bifurcation with no secondary, symmetry-breaking, bifurcations for a nonlinear Neumann boundary-value problem or, equivalently, for an equation involving the conjugate operator, which is the Hilbert transform of functions on the unit circle.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 76A15
Mathematics Subject Classification ID: 82D30
zbMATH DE Number: 1006672
zbMATH Keywords: periodic solutions
zbMATH Keywords: Peierls-Nabarro equation
zbMATH Keywords: Benjamin-Ono equation
zbMATH Keywords: uniqueness of Peierls solution
zbMATH Keywords: global bifurcation
author: John F. Toland
MaRDI profile type: Publication
full work available at URL: jfan.1996.3016
OpenAlex ID: W2050618747
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DOI: 10.1006/JFAN.1996.3016
description: scientific article; zbMATH DE number 1006672