Multi-soliton solution, rational solution of the Boussinesq–Burgers equations

In this paper we consider the Boussinesq–Burgers equations and establish the transformation which turns the Boussinesq–Burgers equations into the single nonlinear partial differential equation, then we obtain an auto-Bäcklund transformation and abundant new exact solutions, including the multi-solitary wave solution and the rational series solutions. Besides the new trigonometric function periodic solutions are obtained by using the generalized tan h method.