含有任意次正幂项非线性广义BBM方程的精确解  

Exact Solutions of the Generalized BBM Equation with any Positive Power Nonlinearity

作　　者：李修勇[1] 王三良[1] 李保安[1] 

机构地区：[1]河南科技大学理学院

出　　处：《河南科技大学学报（自然科学版）》2006年第4期84-87,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：河南省教育厅自然科学基金项目(2006110002);河南科技大学基金项目(2004ZY040);(2004ZD002)和(2001QN13)

摘　　要：利用F-展开法的思想(F是一阶四次常微分方程的一个解),将求含有任意次正幂项非线性广义BBM方程的精确解转化为求一阶四次常微分方程的精确解。并利用一阶四次常微分方程的部分正精确解求得含有任意次正幂项非线性广义BBM方程的一些精确解,包括钟状孤波解、扭状孤波解以及用三角函数表示的周期解。In this paper,by using the idea of F-expansion method(where F is a known solution of an ordinary differential equation with fourth positive power nonlinearity),the problem of seeking the exact solutions of the generalized BBM equation with any positive power nonlinearity is changed into seeking the exact solutions of an ordinary differential equation with fourth positive power nonlinearity.Using some positive solutions of the ODE,the solutions of the generalized BBM equation are obtained,which are the bell type solitary wave solution,the kink type solitary wave solution,and the sinusoidal traveling wave solution.

关 键 词：广义BBM方程 齐次平衡原则 F-展开法 精确解 

分 类 号：O175.2[理学—数学]