摘要
应用李无穷小不变规则,得到了广义变系数KdV-Burgers方程的连续等价变换。从等价代数开始,构造了一阶微分不变量并依据微分不变量对方程作了群分类。最后,通过等价变换将一般的变系数KdV-Burgers方程映射为常系数Burgers方程、KdV方程、KdV-Burgers方程。同时,也得到了变系数KdV-Burgers方程的一些精确解。
By using Lie＇s invariance infinitesimal criterion, the continuous equivalence transformations of a class of nonlinear KdV-Burgers equations with variable coefficients are obtained. The differential invariants of order 1 are constructed and the group classification are made starting from the equivalence algebra. At last some general class of variable coefficient nonlinear KdV-Burgers equations are mapped to constantcoefficient Burgers equation, KdV equation and KdV-Burgers equation. In particular, some exact solutions of the variable coefficients KdV-Burgers equation are obtained.
出处
《量子电子学报》
CAS
CSCD
北大核心
2009年第2期138-147,共10页
Chinese Journal of Quantum Electronics
基金
山东省自然科学基金项目(2004ZX16
Q2005A01)
关键词
非线性方程
李无穷小不变规则
微分不变量
群分类
广义变系数KdV—Burgers方程
nonlinear equation
Lie＇s invariance infinitesimal criterion
differential invariants
group classification
generalized KdV-Burgers equation with variable coefficierts
