(1 + 1)-维Benjiamin Ono方程的行波解及分岔  

Bifurcation and Travelling Wave Solutions for the (1 + 1)-Dimensional Benjiamin Ono Equation

作　　者：杨德牛 

机构地区：[1]南昌应用技术师范学院,江西 南昌

出　　处：《应用数学进展》2022年第11期7503-7511,共9页Advances in Applied Mathematics

摘　　要：本文借助平面动力系统分支理论和符号计算方法研究了(1 + 1)-维的Benjiamin Ono方程。首先经过行波变换得到二维的平面行波系统,借助Maple软件的符号计算得到了分岔的参数条件,同时给出了所有的分岔相图。利用平面行波系统的首次积分,把行波系统的求解转化为椭圆积分。然后讨论了在不同参数条件下所有精确解的解析表达式,包括周期波解、孤立波解,同时也给出了这些解的平面图像,通过图像可以很好的揭示其动力学行为。In the paper, the (1+1)-dimensional Benjiamin Ono equation is studied by means of bifurcation theory and method of plane dynamical systems. Firstly, the traveling wave system are obtained by traveling wave transformation. The parameter conditions of the bifurcation are obtained by the symbolic calculation of Maple software, and all the phase diagrams of the bifurcation are given. By using the first integral of a plane traveling wave system, the solution of the traveling wave system is transformed into an elliptic integral. Then, the analytical expressions of all the exact solutions un-der different parameters are discussed, including periodic wave solutions and solitary wave solu-tions. At the same time, the plane images of these solutions are given, which can reveal their dy-namic behaviors well.

关 键 词：孤立波解 周期波解 非线性发展方程 分岔 

分 类 号：O175[理学—数学]