Solitons, peakons and periodic cusp wave solutions for the Fornberg–Whitham equation

In this paper, we employ the bifurcation method to dynamical systems to investigate the exact travelling wave solutions for the Fornberg–Whitham equation ut−uxxt+ux+uux=uuxxx+3uxuxx.ut−uxxt+ux+uux=uuxxx+3uxuxx. The implicit expression for solitons is given. The explicit expressions for peakons and periodic cusp wave solutions are also obtained. Further, we show that the limits of soliton solutions and periodic cusp wave solutions are peakons.