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

In this paper, the compound Burgers–Korteweg–de Vries equation is studied by the first integral method, which is based on ring theory in commutative algebra. Several new kink-profile waves and periodic waves are established. The applications of these results to other nonlinear wave equations such as the modified Burgers–KdV equation and the compound KdV equation are discussed. The stability and bifurcations of the kink-profile waves are also indicated.