Integrable Curve Motions in n-Dimensional Centro-Affine Geometries

被引：0
作者：
Li Yan-Yan [1 ]
机构：
[1] Xianyang Normal Univ, Inst Math & Informat Sci, Xianyang 712000, Peoples R China
来源：
CHINESE PHYSICS LETTERS | 2010年 / 27卷 / 03期
基金：
中国国家自然科学基金;
关键词：
PLANE-CURVES; KDV EQUATION; SPACE-CURVES; SYSTEMS;
D O I：
10.1088/0256-307X/27/3/030202
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Motions of curves in n-dimensional (n = 4) centro-affine geometries are studied. It is shown that the 1+1-dimensional KdV equations and their hierarchy satisfied by the curvatures of curves under inextensible motions arise from such motions.
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相关论文
共 15 条
[1]   The theory of differential invariants and KdV Hamiltonian evolutions [J].
Beffa, GM .
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1999, 127 (03) :363-391
[2]   Integrable equations arising from motions of plane curves. II [J].
Chou, KS ;
Qu, CZ .
JOURNAL OF NONLINEAR SCIENCE, 2003, 13 (05) :487-517
[3]   Integrable motions of space curves in affine geometry [J].
Chou, KS ;
Qu, CZ .
CHAOS SOLITONS & FRACTALS, 2002, 14 (01) :29-44
[4]   Integrable equations arising from motions of plane curves [J].
Chou, KS ;
Qu, CZ .
PHYSICA D-NONLINEAR PHENOMENA, 2002, 162 (1-2) :9-33
[5]   The KdV equation and motion of plane curves [J].
Chou, KS ;
Qu, CZ .
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2001, 70 (07) :1912-1916
[6]   Exact periodic solitary-wave solution for KdV equation [J].
Dai, Zheng-De ;
Liu, Zhen-Jiang ;
Li, Dong-Long .
CHINESE PHYSICS LETTERS, 2008, 25 (05) :1531-1533
[7]   THE KORTEWEG-DEVRIES HIERARCHY AS DYNAMICS OF CLOSED CURVES IN THE PLANE [J].
GOLDSTEIN, RE ;
PETRICH, DM .
PHYSICAL REVIEW LETTERS, 1991, 67 (23) :3203-3206
[8]   SOLITON ON A VORTEX FILAMENT [J].
HASIMOTO, H .
JOURNAL OF FLUID MECHANICS, 1972, 51 (FEB8) :477-&
[9]  
LAMB GL, 1977, J MATH PHYS, V18, P1654, DOI 10.1063/1.523453
[10]   Higher-dimensional integrable systems induced by motions of curves in affine geometries [J].
Li Yan-Yan ;
Qu Chang-Zheng .
CHINESE PHYSICS LETTERS, 2008, 25 (06) :1931-1934
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