Bäcklund Transformations for Integrable Geometric Curve Flows

Symmetry

Changzheng Qu²  Jingwei Han¹  Jing Kang³ 

[1] School of Information Engineering, Hangzhou Dianzi University, Hangzhou 310018, China; E-Mail:;Department of Mathematics, Ningbo University, Ningbo 315211, China;Department of Mathematics, Northwest University, Xi’an 710069, China; E-Mail:

关键词: invariant geometric flow;    Bäcklund transformation;    integrable system;    differential invariant;   

DOI  :  10.3390/sym7031376

来源: mdpi

【 摘 要 】

We study the Bäcklund 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 Schrödinger 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 Bäcklund transformations relating to these two integrable geometric flows. Some special solutions of the integrable systems are used to obtain the explicit Bäcklund transformations.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.