首页 | 本学科首页   官方微博 | 高级检索  
     检索      

常挠率运动曲线生成曲面上的贝克隆变换
引用本文:曹锡芳,徐传友.常挠率运动曲线生成曲面上的贝克隆变换[J].数学物理学报(A辑),2014,34(1):115-125.
作者姓名:曹锡芳  徐传友
作者单位:扬州大学数学科学学院 江苏 扬州 225002
基金项目: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.
收稿时间:2012-04-12
修稿时间:2013-08-19

B\"acklund Transformations on Surfaces Swept outby Moving Curves with Constant Torsion
CAO Xi-Fang,XU Chuan-You.B\"acklund Transformations on Surfaces Swept outby Moving Curves with Constant Torsion[J].Acta Mathematica Scientia,2014,34(1):115-125.
Authors:CAO Xi-Fang  XU Chuan-You
Institution:Department of Mathematics, Yangzhou University, Jiangsu Yangzhou 225002
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.
Keywords:Motion of curveszz  Curvature and torsionzz  Integrable systemzz  B\"  acklund transformationzz
本文献已被 CNKI 等数据库收录!
点击此处可从《数学物理学报(A辑)》浏览原始摘要信息
点击此处可从《数学物理学报(A辑)》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号