Boussinesq方程组的行波解研究

Study on bifurcations of traveling wave solutions of Boussinesq equation

运用动力系统定性理论,提出一种分析非线性系统解的方法.并以Boussinesq方程为例,避免了求解的繁琐过程,得到解的几何特性.分析结果表明,在一定参数条件下,Boussinesq方程的相图中存在孤波、扭结波以及周期波.

By using the qualitative theory of dynamical systems, a method is advanced to analyze the solutions of the non- linear systems. Appling this method to Boussinesq equations, the geometry shapes of the equation solutions are obtained, and the fussy process of solving equations is avoided. It is also found that under certain parametrieal conditions, different phase portraits of Boussinesq equations exist, including bifurcations of solitary waves, kink waves and periodic waves.