BBM方程的精确行波解研究  

Study on the exact traveling wave solution of the BBM equation

作　　者：刘红霞 韩青秀 伍芸 于亚峰 LIU Hongxia;HAN Qingxiu;WU Yun;YU Yafeng(School of Mathematical Sciences,Guizhou Normal University,Guiyang,Guizhou 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《贵州师范大学学报（自然科学版）》2022年第2期71-75,共5页Journal of Guizhou Normal University：Natural Sciences

摘　　要：利用动力系统分支理论研究了BBM方程u_(t)+αu_(x)+βuu_(x)-γ_(xxt)^(u)=0。首先通过行波变换,求得方程的首次积分和奇点,其次对平衡点分析得到系统的相图,再次对其轨道进行分析,进而得到这些系统所有可能存在的行波解,包括孤立波解、周期波解。We study the BBM equation u_(t)+αu_(x)+βuu_(x)-γ_(xxt)^(u)=0 by using the dynamical system branching theory.First,the first integration and the singularity of the equation are obtained through the traveling wave transformation,followed by the equilibrium point analysis of the phase diagram of the system.The orbits are analyzed again,and then all possible traveling wave solutions of these systems are obtained,including isolated wave solutions,periodic wave solutions.

关 键 词：动力系统 BBM方程 非线性波 孤立波 周期波 

分 类 号：O175.29[理学—数学]