变系数广义Gardner方程的微分不变量及群分类  

Differential invariants and group classification of variable coefficient generalized Gardner equation

作　　者：郭美玉[1] 高洁[1] 

机构地区：[1]聊城大学数学科学学院,聊城252059

出　　处：《物理学报》2009年第10期6686-6691,共6页Acta Physica Sinica

基　　金：山东省自然科学基金(批准号:2004ZX16;Q2005A01)资助的课题~~

摘　　要：应用李无穷小不变规则,得到了变系数广义Gardner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,通过等价变换将变系数Gardner方程映射为常系数mKdV方程、KdV-mKdV方程.同时,也得到了变系数广义Gardner方程的一些精确解.By using Lie s invariance infinitesimal criterion,we obtain the continuous equivalence transformations of a class of nonlinear Gardner equations with variable coefficients.Starting from the equivalence algebra,we construct the differential invariants of order one and make group classification.Finally some general class of variable coefficient nonlinear Gardner equations can be mapped to constant-coefficient mKdV equation and KdV-mKdV equation.In particular,some exact solutions of t the Gardner equation with variable coefficients are obtained.

关 键 词：李无穷小不变规则 微分不变量 群分类 变系数广义Gardner方程 

分 类 号：O175[理学—数学]