广义Boussinesq方程的光滑孤子解和各种周期行波解  

Smooth soliton solutions and different kinds of periodic traveling wave solutions for a generalized Boussinesq equation

作　　者：芮伟国[1] 冀小明[2] 谢绍龙[3] 

机构地区：[1]红河学院数学系,云南蒙自661100 [2]西南民族大学预科教育学院,四川成都610041 [3]玉溪师范学院数学系,云南玉溪653100

出　　处：《西南民族大学学报（自然科学版）》2007年第6期1229-1235,共7页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10571062);云南省教育厅自然科学基金资助项目(06Y147A).

摘　　要：本文利用平面动力系统分支理论和Jacobi椭圆函数法,研究了一类广义Boussinesq方程.在不同的参数条件下,绘出了各种分支相图,利用这些相图,讨论了各种行波解的存在性.通过相图中的各种轨道,获得了孤立波,扭子波和周期波的精确解.In this paper, using the theory of planar dynamical system and the method of Jacobian elliptic function, the generalized Boussinesq equation is studied. Under different parametric conditions, all kinds of bifurcations of phase portraits are given. By using these phase portraits, the existence which is all kinds of traveling wave solutions is discussed. By the orbit in the phase portraits, different kinds of solitary wave, kink wave and periodic wave solutions are obtained.

关 键 词：广义BOUSSINESQ方程 孤立波 扭子波 周期波 动力系统分支理论 

分 类 号：O175.2[理学—数学]