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

LI Yanyan

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

更新时间：2023-12-11

- Higher Dimensional Integrable Equation Induced by Motion of Curves in Four-Dimensional Centro-Affine Geometry
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 50, Issue 2, Pages: 25-27(2011)
- 作者机构：
  
  咸阳师范学院数学与信息科学学院,陕西,咸阳,712000
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2011，
  
  Published Online：25 March 2011，
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LI Yanyan. Higher Dimensional Integrable Equation Induced by Motion of Curves in Four-Dimensional Centro-Affine Geometry. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 50(2):25-27(2011)
DOI：

LI Yanyan. Higher Dimensional Integrable Equation Induced by Motion of Curves in Four-Dimensional Centro-Affine Geometry. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 50(2):25-27(2011) DOI：

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。

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.

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

Keywords

centro-affine geometryintegrable equationinvariant curve flowbreaking soliton equation

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