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

作　　者：杨云青 王云虎 李昕 程雪苹 

机构地区：[1]School of Mathematics, Physics and Information Science, Zhejiang Ocean University [2]Shanghai Key Laboratory of Trustworthy Computing, East China Normal University [3]School of Mathematics and Statistics, Changshu Institute of Technology

出　　处：《Chinese Physics B》2014年第3期186-192,共7页中国物理B（英文版）

基　　金：Project supported by the Zhejiang Provincial Natural Science Foundation of China(Grant Nos.LQ12A01008 and LY12A01010)

摘　　要：We extend the method of constructing Bgcklund 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 Backlund 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. Es- pecially, some classical equations such as the cylindrical KdV equation are just the special cases of the constrain condition.We extend the method of constructing Bgcklund 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 Backlund 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. Es- pecially, some classical equations such as the cylindrical KdV equation are just the special cases of the constrain condition.

关 键 词：Baicklund transformation Lax pair conservation law Cole-Hopf transformation 

分 类 号：O175[理学—数学]