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.