Equations of Camassa-Holm type and the geometry of loop groups
type: Item
instance of: scholarly article
title: Equations of Camassa-Holm type and the geometry of loop groups
zbMATH Open document ID: 1332.35088
author: Przemysław Górka
author: Daniel J. Pons
author: Enrique G. Reyes
published in: Journal of Geometry and Physics
publication date: 2014-12-03T00:00:00Z
review text: The authors investigate equations on groups, specially loop groups, motivated by some of Arnold's classical work on the Riemannian geometry of diffeomorphism groups. They prove easily computable formulae for the sectional curvature in the case of the diffeomorphism group of the circle, and observe that this group has a \(CR\)-manifold structure. There are also presented examples of bona fide Hamiltonian equations in infinitely many derivatives.
Mathematics Subject Classification ID: 35G50
Mathematics Subject Classification ID: 22E67
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 35R03
Mathematics Subject Classification ID: 35Q31
Mathematics Subject Classification ID: 32V20
zbMATH DE Number: 6376722
zbMATH Keywords: Camassa-Holm equation
zbMATH Keywords: diffeomorphism group
zbMATH Keywords: sectional curvature
zbMATH Keywords: equations with infinitely many derivatives
zbMATH Keywords: Euler equation on Lie groups
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: j.geomphys.2014.07.028
OpenAlex ID: W2023931774
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DOI: 10.1016/J.GEOMPHYS.2014.07.028
description: scientific article; zbMATH DE number 6376722