带高阶色散项的双非线性水波方程的新孤立波解  

New Soliton Wave Solutions for the Bilinear Water Wave Equation with High-order Dispersive

作　　者：青君[1] 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)

机构地区：[1]广州铁路职业技术学院基础课部,广州510430 [2]华东师范大学数学科学学院,上海200241 [3]四川师范大学数学科学学院,成都610066

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)。

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.

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 

分 类 号：O175.29[理学—数学]