变系数G展开法与广义浅水波方程的精确解

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英文篇名：Variable coefficient G expansion method and exact solutions for the generalized shallow water wave equation 作者：王鑫 ; 岳晓蕊 英文作者：WANG Xin;YUE Xiaorui;College of Information Science and Technology,Hainan University; 关键词：广义浅水波方程 ; G展开法 ; 精确解 ; 变系数 英文关键词：generalized shallow water wave equation;;G expansion method;;exact solutions;;variable coefficients 中文刊名：FZDZ 英文刊名：Journal of Fuzhou University(Natural Science Edition) 机构：海南大学信息科学技术学院; 出版日期：2019-01-09 13:49 出版单位：福州大学学报(自然科学版) 年：2019 期：v.47;No.227 基金：海南省自然科学基金资助项目(117066);; 国家自然科学基金资助项目(11601109);; 海南省科协青年科技英才学术创新计划资助项目(201503) 语种：中文; 页：FZDZ201901001 页数：6 CN：01 ISSN：35-1117/N 分类号：5-10

摘要

以(G'/G)的基本思想为依据,构造了一种变系数G展开法,即(G-G'/G+G')展开法,其中的函数G满足一类二阶变系数非线性常微分方程.通过此展开法,并借助Mathematica计算软件,对广义浅水波方程进行了求解,获得了该方程显式行波解.事实证明,变系数G展开法对于求解非线性偏微分方程的精确解是有效可行的.
        In this paper,based on the basic idea of the(G'/G) expansion method,a class variable coefficient G expansion method is constructed,that is the (G-G'/G+G')expansion method,which satisfies a class of two order nonlinear ordinary differential equations with variable coefficients. Through this expansion method,the generalized shallow water wave equation is solved with the help of the calculation software Mathematica,and the explicit traveling wave solutions of the equation are obtained. It is proved that the variable coefficient G expansion method is effective and feasible for solving the exact solutions of the nonlinear partial differential equations.

引文

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