Bifurcations and exact traveling wave solutions for the KdV-like equation

Applying the combination of the qualitative theory of differential equation and bifurcation theory of planar dynamical systems to a combined form of KdV-like equation, the bifurcations of phase portraits to the corresponding traveling system of this equation are presented. The exact representations of smooth and non-smooth traveling wave solutions are obtained under different regions of parametric space. Moreover, numerical simulations are provided for some solutions of the equation.