变系数KdV-Burgers方程的精确解及其Bcklund变换  

Exact Solution and Bcklund Transformation of Variable Coefficients KdV-Burgers Equation

作　　者：王燕[1] 孙福伟[1] 

机构地区：[1]北方工业大学理学院,北京100144

出　　处：《北方工业大学学报》2009年第3期45-50,共6页Journal of North China University of Technology

摘　　要：利用Painlevé分析方法,借助计算机符号运算,研究了广义变系数KdV-Burgers方程,得出该方程的可积条件,从而获得变系数间的约束条件.求得该变系数方程的Backlund变换,得到了一般变系数KdV-Burgers方程精确解的表达式,从而得到其单孤子解、双孤子解、三孤子解等,并给出了相关的孤子变化图形.With the Painleve test method and computer symbolic computation, the paper stud- ies the generalized variable coefficients KdV-Burgers equation to obtain the integral conditions of that equation and the binding conditions between the variable coefficients. Then, the B^icklund transformation of that variable coefficients equation and the exact solution of the equation expres- sion of the general variable coefficients KdV-Burgers are determined, from which the single-, two-, three-, and etc. soliton solutions are obtained and related graphic changes in the solution are given.

关 键 词：变系数KdV-Burgers方程 PAINLEVÉ分析 Bcklund变换 精确解 孤子解 

分 类 号：O175[理学—数学]