Integrable equations arising from motions of plane curves

被引：167
作者：
Chou, KS [1 ]
Qu, CZ
机构：
[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
[2] NW Univ Xian, Dept Math, Xian 710069, Peoples R China
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2002年 / 162卷 / 1-2期
基金：
美国国家科学基金会;
关键词：
integrable equations; motion of plane curves; Klein geometry; Lie algebra; traveling wave;
D O I：
10.1016/S0167-2789(01)00364-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The motion of plane curves in Klein geometry is studied. It is shown that the KdV, Harry-Dym, Sawada-Kotera, Burgers, the defocusing mKdV hierarchies, the Camassa-Holm and the Kaup-Kupershmidt equation naturally arise from the motions of plane curves in SL(2)-, Sim(2)-, SA(2)- and A(2) -geometries. These local and nonlocal dynamics conserve global geometric quantities of curves such as perimeter and enclosed area. Motions of curves in Euclidean, special linear and similarity geometries corresponding to the traveling wave solutions of the mKdV, KdV and Burgers equations are discussed. (C) 2002 Elsevier Science B.V All rights reserved.
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页码：9 / 33
页数：25
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