Smooth and non-smooth traveling wave solutions of the Fornberg–Whitham equation with linear dispersion term

In this paper, the Fornberg–Whitham equation with linear dispersion term is investigated by employing the bifurcation method of dynamical systems. As a result, the existence of smooth and non-smooth traveling wave solutions is obtained. And the analytic expressions of solitary wave solutions, periodic cusp wave solutions and peakons are given under some parameter conditions.