广义变系数Kawachara方程的等价变换、精确解和守恒律  

Equivalent Transformation,Exact Solution and Conservation Law of Generalized Kawachara Equation with Variable Coefficient

作　　者：常丽娜 刘汉泽[1] CHANG Li-na;LIU Han-ze(School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,China)

机构地区：[1]聊城大学数学科学学院

出　　处：《聊城大学学报（自然科学版）》2020年第2期11-17,共7页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目（11171041）资助

摘　　要：利用改进的CK方法将广义变系数Kawachara方程约化为常系数Kawachara方程,得到等价变换.应用李群分析求出了该方程的李对称和约化方程,并对约化方程求其精确解,进而得到了变系数Kawachara方程的精确解.最后给出了该方程的守恒律.In this paper,the Kawachara equation with generalized variable coefficient is reduced to the Kawachara equation with constant coefficient by the improved CK method,and equivalent transformation is obtained.By using Lie group analysis,the Lie symmetric and reductive equation of the equation is obtained,and the exact solution of the reductive equation is obtained,and then the exact solution of the Kawachara equation with variable coefficients is obtained.finally,the conservation law of the equation is given.

关 键 词：广义变系数Kawachara方程 等价变换 对称约化 精确解 守恒律 

分 类 号：O175.2[理学—数学]