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Chin. Phys. B, 2014, Vol. 23(3): 030506    DOI: 10.1088/1674-1056/23/3/030506
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Riccati-type Bäcklund transformations of nonisospectral and generalized variable-coefficient KdV equations

Yang Yun-Qinga, Wang Yun-Hub, Li Xinc, Cheng Xue-Pinga
a School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316004, China;
b Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;
c School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, China
Abstract  We extend the method of constructing Bäcklund transformations for integrable equations through Riccati equations to the nonisospectral and the variable-coefficient equations. By taking nonisospectral and generalized variable-coefficient Korteweg–de Vries (KdV) equations as examples, their Bäcklund transformations are obtained under a more generalized constrain condition. In addition, the Lax pairs and infinite numbers of conservation laws of these equations are given. Especially, some classical equations such as the cylindrical KdV equation are just the special cases of the constrain condition.
Keywords:  Bäcklund transformation      Lax pair      conservation law      Cole–Hopf transformation  
Received:  09 July 2013      Revised:  08 August 2013      Accepted manuscript online: 
PACS:  05.45.Yv (Solitons)  
  02.30.Ik (Integrable systems)  
Fund: Project supported by the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LQ12A01008 and LY12A01010).
Corresponding Authors:  Yang Yun-Qing     E-mail:  yqyang@amss.ac.cn

Cite this article: 

Yang Yun-Qing, Wang Yun-Hu, Li Xin, Cheng Xue-Ping Riccati-type Bäcklund transformations of nonisospectral and generalized variable-coefficient KdV equations 2014 Chin. Phys. B 23 030506

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