Soliton curves in three-dimensional space forms
Soliton curves in three-dimensional space forms
复制标题
三维空间形式的孤子曲线
DOI：
10.1016/j.geomphys.2018.07.014
复制
发表时间：
2018
影响因子：
1.5
通讯作者：
Satoshi Kawakubo
中科院分区：
文献类型：
--
作者：
Yasushi Homma;本間泰史;Satoshi Kawakubo
定域诱导方程是以涡丝运动为模型的空间曲线的几何演化方程，定域诱导方程族是定域诱导方程的可积族。与定域感应族相联系的第n阶定常方程的解称为第n阶孤子曲线。本文研究了三维单连通空间形式中的孤子曲线。特别地，我们给出了n阶孤子曲线的自然曲率的显式表达式。
The localized induction hierarchy is the integrable hierarchy for the localized induction equation, a geometric evolution equation for space curves modeled on the motion of vortex filaments. A solution of the n th stationary equation associated to the localized induction hierarchy is called an n th soliton curve. In this paper, we consider soliton curves in simply-connected three-dimensional space forms. In particular, we give explicit expressions of n th soliton curves in terms of the natural curvatures.