数学物理学报 ›› 2014, Vol. 34 ›› Issue (1): 115-125.

• 论文 • 上一篇    下一篇

常挠率运动曲线生成曲面上的贝克隆变换

曹锡芳, 徐传友   

  1. 扬州大学数学科学学院 江苏 扬州 225002
  • 收稿日期:2012-04-12 修回日期:2013-08-19 出版日期:2014-02-25 发布日期:2014-02-25
  • 基金资助:

    国家自然科学基金(11071208)资助.

B\"acklund Transformations on Surfaces Swept out by Moving Curves with Constant Torsion

 CAO Xi-Fang, XU Chuan-You   

  1. Department of Mathematics, Yangzhou University, Jiangsu Yangzhou 225002
  • Received:2012-04-12 Revised:2013-08-19 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    国家自然科学基金(11071208)资助.

摘要:

该文给出由常挠率运动曲线生成曲面上的贝克隆变换,其中运动曲线的曲率满足修正KdV方程,从而得到著名的对于修正KdV方程贝克隆变换的一个几何实现. 作为应用, 取圆柱面作为种子曲面, 构造了一些由周期运动曲线生成的新曲面, 其中周期运动曲线在xy平面上的投影是闭曲线.

关键词: 曲线运动, 曲率和挠率, 可积系统, 贝克隆变换

Abstract:

We give B\"acklund transformations on surfaces which are swept out by moving curves with constant torsion. The curvature of the moving curve discussed in this paper is governed by the modified KdV equation. Our result can be regarded as a geometric realization of the well-known B\"acklund transformation for the modified KdV equation. As applications, by taking the circular cylinder as a seed surface, we construct some novel surfaces which are swept out by
moving periodic curves whose projections to the xy-plane are closed.

Key words: Motion of curves, Curvature and torsion, Integrable system, B\"acklund transformation

中图分类号: 

  • 53A05