Bäcklund Transformations for Integrable Geometric Curve Flows
Bäcklund Transformations for Integrable Geometric Curve Flows
复制标题
DOI：
10.3390/sym7031376
复制
发表时间：
2015-08
期刊：
影响因子：
--
通讯作者：
C. Qu;Jingwei Han;Jing Kang
中科院分区：
文献类型：
--
作者：
C. Qu;Jingwei Han;Jing Kang
研究了某些几何中可积几何曲线流的Backlund变换。这些曲线流包括二维中心等仿射几何中的KdV流和Camassa-Holm流、二维欧氏几何中的mKdV流和修正Camassa-Holm流、三维欧氏几何中的Schrodinger流和扩展Harry-Dym流以及仿射几何中的Sawada-Kotera流等。利用给定几何中的两条不同曲线受同一可积方程支配的事实，我们得到了与这两个可积几何流有关的Backlund变换。利用可积系统的一些特解，得到了显式的Backlund变换.
We study the Backlund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrodinger and extended Harry-Dym flows in the three-dimensional Euclidean geometry and the Sawada-Kotera flow in the affine geometry, etc. Using the fact that two different curves in a given geometry are governed by the same integrable equation, we obtain Backlund transformations relating to these two integrable geometric flows. Some special solutions of the integrable systems are used to obtain the explicit Backlund transformations.