Shock wave solutions of the compound Burgers–Korteweg–de Vries equation

In this paper, shock wave solutions of the compound Burgers–KdV equation is studied by using qualitative theory of differential equation and ansatz method. The existence and uniqueness of different types of travelling waves of the system are obtained by analyzing qualitatively the existence and uniqueness of the heteroclinic trajectories of the ordinary differential equation. We construct some travelling wave solutions and indicate their stability and bifurcation.