摘要
本文主要研究一类带高阶色散项的双非线性水波方程,它描述了浅水环境下流体的运动。为寻求该方程的精确孤立波解,首先做行波变换将此方程转化为常微分方程。其次,对于一般的m+k=1,选取恰当的变换将此问题归结到四次幂非线性项常微分方程的求解。最后,利用四阶多项式完全判别系统方法得到了上述双非线性水波方程的6组新孤立波解。
This paper mainly talks about the bilinear water wave equation with high-order dispersive,which models the moving of fluid in shallow water.Firstly,the bilinear water wave equation with high-order dispersive is reduced to ordinary differential equation by travelling wave transformation so as to obtain an accurate Soliton wave solution.Then,in the general case of m+k=1,the problem is attributed to solving ordinary differential equation whose nonlinearity is fourth power by a proper transformation.Finally,six pairs of new Soliton wave solutions for the above bilinear water wave equations are obtained by fourth-order polynomial complete-discriminant system method.
作者
青君
何晓燕
朱世辉
QING Jun;HE Xiaoyan;ZHU Shihui(Department of Fundamental Education,Guangzhou Railway Polytechnic,Guangzhou 510430,China;School of Mathematical Sciences,East China Normal University,Shanghai 200241,China;School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,China)
出处
《西华师范大学学报（自然科学版）》
2020年第2期172-178,共7页
Journal of China West Normal University(Natural Sciences)
基金
国家自然科学基金项目(11871138)
广州铁路职业技术学院教改项目(GTXYJ1702)。
关键词
浅水波方程
双线性
孤立波解
多项式完全判别系统方法
shallow water wave equation
bilinear
Soliton wave solution
polynomial complete-discriminant system method
