修正Benjamin-Bona-Mahony方程的精确行波解  

The Exact Traveling Wave Solution of the Modified Benjamin-Bona-Mahony Equation

作　　者：杨春飞 刘小华 YANG Chunfei;LIU Xiaohua(College of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳550025

出　　处：《内蒙古师范大学学报（自然科学版）》2024年第5期532-541,共10页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：贵州省教育厅自然科学研究资助项目“贵州省高等学校光通讯系统中孤子的数学理论与计算协作创新团队”(黔教技[2023]062号)。

摘　　要：利用平面动力系统理论,研究修正Benjamin-Bona-Mahony (mBBM)方程行波解的存在性,得到不同参数条件下的相图和行波解的存在条件。运用广义Riccati辅助方程法给出mBBM方程的双曲解、三角解和有理函数解。并利用Maple软件,分析扭状孤波解、周期解的性状,数值上验证了精确行波解的表达式。The existence of the traveling wave solution of the modified Benjamin-Bona-Mahony(mBBM) equation is studied by using the theory of plane dynamical systems.The phase diagram and conditions for the existence of the traveling wave solution are obtained under different parameters.The generalized Riccati auxiliary equation method is used to derive double perversion,trigonometric,and rational function solutions for the mBBM equation.The properties of torsional solitary wave and periodic wave solutions are analyzed by using Maple software,and numerical verification confirms the expression of exact traveling wave solution.

关 键 词：MBBM方程 解的存在性 广义Riccati辅助方程法 行波解 

分 类 号：O175.29[理学—数学]