一类Benjamin-Bona-Mahony方程的精确行波解  

The Exact Traveling Wave Solutions for a Class of Benjamin-Bona-Mahony Equation

作　　者：任莹蓉 章丽娜[1] REN Yingrong;ZHANG Lina(School of Science,Huzhou University,Huzhou 313000,China)

机构地区：[1]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2018年第8期1-5,共5页Journal of Huzhou University

基　　金：国家自然科学基金面上项目(61473332)

摘　　要：利用平面动力系统分支理论对Benjamin-Bona-Mahony(BBM)方程的精确行波解进行研究.首先对BBM方程进行行波变换,求得其对应行波系统的首次积分与奇点;接着作出在各种参数条件下的相图分支;最后利用相图和首次积分,求得BBM方程在某些参数条件下的孤立波解和光滑周期波解的精确表达式.In this paper, the Benjamin Bona Mahony （BBM） equation is studied. The method is mainly based on the theory of plane dynamic systems. By making traveling transformation to the BBM equation, we obtain the first integral and the singular points of the corresponding traveling wave system. Furthermore, we draw the phase portraits under certain parameter conditions. Finally, we obtain the exact parametric expressions of solitary wave solutions and smooth periodic wave solutions for the BBM equation.

关 键 词：平面动力系统 相图 光滑周期波解 光滑孤立波解 

分 类 号：O175[理学—数学]