Riccati-type Bäcklund transformations of nonisospectral and generalized variable-coefficient KdV equations

doi:10.1088/1674-1056/23/3/030506

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 (杨云青), Wang Yun-Hu (王云虎), Li Xin (李昕), Cheng Xue-Ping (程雪苹) Riccati-type Bäcklund transformations of nonisospectral and generalized variable-coefficient KdV equations 2014 Chin. Phys. B 23 030506

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Riccati-type Bäcklund transformations of nonisospectral and generalized variable-coefficient KdV equations

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