Travelling wave solutions of the Fornberg–Whitham equation

Zhou and Tian [J.B. Zhou, L.X. Tian, A type of bounded travelling wave solutions for the Fornberg–Whitham equation, J. Math. Anal. Appl. 346 (2008) 255–261] successfully found a type of bounded travelling wave solutions of the Fornberg–Whitham equation. In this paper, we improve the previous result by using the phase portrait analytical technology. Moreover, some smooth periodic wave, smooth solitary wave, periodic cusp wave and loop-soliton solutions are given, and the numerical simulation is made. The results show that our theoretical analysis agrees with the numerical simulation.