Integrable motions of space curves in affine geometry
type: Item
instance of: scholarly article
title: Integrable motions of space curves in affine geometry
zbMATH Open document ID: 1014.37047
DOI: 10.1016/S0960-0779(01)00179-5
author: Kai-Seng Chou
author: Changzheng Qu
published in: Chaos, Solitons and Fractals
publication date: 2002-08-18T00:00:00Z
review text: Relations between motions of curves and soliton equations are interesting to not only mathematicians but also physicists. In the affine geometry direction, we have as samples the work of Chern and Terng in 1980 giving an affine analog of the Bäcklund transformation, and that of Pinkall in 1995 realizing the KdV equation as a Hamiltonian curve flow which keeps the total centro-affine curvature invariant. The authors of this articie under review connect motions of curves in affine and centro-affine three-dimensional spaces to the Korteweg-de Vries, Harry-Dym, and Sawada-Kotera hierarchies, as well as the Boussinesq, Kaup-Kupershmidt, Tzitzeica, and Hirota-Satsuma equations. Moreover, they explicitly construct the motions of curves corresponding to the soliton solutions of the KdV and Sawada-Kotera equations.
reviewed by: Hongyou Wu
Mathematics Subject Classification ID: 37K25
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 1783200
zbMATH Keywords: curves in affine geometry
zbMATH Keywords: motions of curves
zbMATH Keywords: soliton equations
MaRDI profile type: Publication
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full work available at URL: s0960-0779(01)00179-5
OpenAlex ID: W2071877482
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description: scientific article; zbMATH DE number 1783200