尘埃等离子体中扩展的ZK方程的最优系统和幂级数解  

Optimal Systems and Power Series Solutions of the Extended ZK Equation in Dusty Plasmas

作　　者：高芳 GAO Fang(School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《滨州学院学报》2021年第4期65-71,共7页Journal of Binzhou University

基　　金：国家自然科学基金项目(11101115);山东省自然科学基金联合专项项目(ZR2015AL008)。

摘　　要：应用经典李对称方法研究尘埃等离子体中扩展的ZakharovKuznetsov方程的最优系统、精确解和幂级数解。首先,通过李对称分析求得了一维最优系统;其次,通过相似约简得到群不变解,然后对群不变解进行第二次李对称分析,解得了方程的精确解;最后,应用幂级数方法获得了方程的显示解。The classical Lie symmetry method is used to study the optimal system,the exact solution and power series solution of the extended Zakharov-Kuznetsov equation in dusty plasmas.Firstly,the one-dimensional optimal system is obtained by Lie symmetry analysis.Secondly,the group invariant solution is solved by similarity reduction,and then the second Lie symmetry analysis is carried out to obtain the exact solution of the equation.Finally,the explicit solution of the equation is obtained by power series method.

关 键 词：尘埃等离子体 ZakharovKuznetsov方程 李对称分析 最优系统 幂级数解 

分 类 号：O175[理学—数学]