含任意次正幂项的广义五阶KdV方程的精确解  

Exact solutions to the generalized fifth order KdV equations with arbitrary positive power nonlinearities

作　　者：李灵晓[1] 张金良[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳4710003

出　　处：《纯粹数学与应用数学》2010年第5期811-815,871,共6页Pure and Applied Mathematics

基　　金：河南省国际合作交流项目(084300510060);河南科技大学青年科研基金(2008QN026)

摘　　要：利用齐次平衡原理,通过引进含非线性辅助微分方程(sub-ODE),获得了含任意次正幂项的广义五阶KdV方程的精确解,包括钟状孤波解,扭状孤波解和三角函数表示的周期波解.所得精确解与前人用其它方法所获得一致,并包含了以往文献未提供的部分解,扩充并完善了以往文献的相关结果.With the aid of homogeneous balance principle and a nonlinear subsidiary ordinary differential equation （sub-ODE）, the exact solutions to the generalized fifth order KdV equations with arbitrary positive power nonlinearities are found out. The solutions are expressed by the bell type solitary wave solutions, the kink type solitary wave solutions and the trigonometric functional periodic solutions. Exact solutions obtained by other methods with the previous unanimous, and includes some of the previous literature does not provide solutions to expand and improve the results of previous studies related.

关 键 词：广义五阶KDV方程 含任意项非线性辅助微分方程 精确解 齐次平衡 

分 类 号：O175[理学—数学]