Bifurcation of travelling wave solutions for the (2 + 1)-dimensional Broer–Kau–Kupershmidt equation

The bifurcation method of planar dynamical systems and numerical simulation method of differential equations are employed to investigate the (2 + 1)-dimensional Broer–Kau–Kupershmidt equation. We obtain the sufficient conditions to guarantee the existence of the bounded travelling wave solutions including solitary wave solutions, kink or anti-kink wave solutions and periodic wave solutions. Furthermore, under different parameter conditions, the qualitatively different phase portraits are given and the corresponding bounded travelling waves are simulated.