Boussinesq方程的精确孤子解研究

Study on exact soliton solution of Boussinesq equation

本文通过Jumarie的改性Riemann Liouville导数构建时间分数阶Boussinesq方程;应用函数变量法得到了这些时间分数阶方程的精确孤子解,这些精确解可以描述周期波和孤立波;导出的解在海洋工程中有许多潜在的应用,结果表明函数变量法求解分数阶微分方程简单有效。

In this paper, time-fractional Boussinesq-like equations are constructed via Jumarie＇s modified Riemann-Liouville derivative. The functional variable method is applied to obtain exact soliton solutions of these time-fractional equations. These exact solutions can describe periodic and soliton waves. The derived solutions address many potential applications in ocean engineering and the results show that the functional variable method is simple and efficient to solve fractional differential equations.