Bifurcations and exact bounded travelling wave solutions for a partial differential equation

In this paper, a partial differential equation is investigated by using the bifurcation theory and the method of phase portraits analysis, the existence of loop soliton, peakon, generalized compacton, smooth and non-smooth periodic waves, breaking kink and anti-kink waves is proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some conditions, exact parametric representations of these waves in explicit and implicit forms are obtained.