中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (2): 25-27.

• 研究论文 • 上一篇    下一篇

四维中心仿射几何中由曲线运动导出的高维可积方程

李艳艳

  

  1. (咸阳师范学院数学与信息科学学院,陕西 咸阳 712000)
  • 收稿日期:2010-03-09 修回日期:1900-01-01 出版日期:2011-03-25 发布日期:2011-03-25

Higher Dimensional Integrable Equation Induced by Motion of Curves in Four-Dimensional Centro-Affine Geometry

LI Yanyan   

  1. (Institute of Mathematics and Information Science, Xianyang Normal University,Xianyang 712000, China)
  • Received:2010-03-09 Revised:1900-01-01 Online:2011-03-25 Published:2011-03-25

摘要: 讨论了四维中心仿射几何中由2+1维的曲线运动导出的高维可积方程。这种曲线运动是通过对四维中心仿射几何中1+1维的曲线运动公式增加一个额外的空间变量y得到的, 它等价于四维中心仿射几何中的曲面运动。证明了2+1维的可积破裂孤立子方程来自于四维中心仿射几何中的这种曲线运动。不仅将已有的三维中心仿射几何中的这种曲线运动推广到了四维中心仿射几何, 还丰富了对2+1维的破裂孤立子方程的几何解释。

关键词: 中心仿射几何, 可积方程, 不变曲线流, 破裂孤立子方程

Abstract: The higher-dimensional integrable equation induced by the 2+1-dimensional motion of curves in four-dimensional centro-affine geometry is discussed. The curves motion is obtained by adding an extra space variable y to the 1+1-dimensional curves motion in four-dimensional centro-affine geometry, which is equivalent to the surface motion in four-dimensional centro-affine geometry. It is shown that the 2+1-dimensional breaking soliton equation arises from such motion in four-dimensional centro-affine geometry.The result not only extends the existing curve motion in three-dimensional centro-affine geometry to four-dimensional centro-affine geometry, but also enriches geometric explanation of the 2+1-dimensional breaking soliton equation.

Key words: centro-affine geometry, integrable equation, invariant curve flow, breaking soliton equation

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