CTE method to the interaction solutions of Boussinesq–Burgers equations

Abstract

Under investigation in this paper is the Boussinesq–Burgers equations, which describe the propagation of shallow water waves. Via the truncated Painlevé analysis and the consistent tanh expansion (CTE) method, some exact interaction solutions among different nonlinear excitations such as multiple resonant soliton solutions, soliton–error function waves, soliton–periodic waves, soliton–rational waves, and soliton–potential Burgers waves are explicitly given.