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.