Bilinear form and new multi-soliton solutions of the classical Boussinesq–Burgers system

In this paper, we study the multi-soliton solutions and their interactions of the classical Boussinesq–Burgers (CBB) system describing propagations of shallow water waves. Based on the Hirota bilinear method, we obtain new multi-soliton solutions of the CBB system. By using asymptotic analysis, we find that the interactions of the multi-soliton solutions are purely elastic. The interactions are shown graphically. We also find that the multi-soliton solution types may depend on the parameter in the CBB system.