New families of travelling wave solutions for Boussinesq–Burgers equation and ()-dimensional Kadomtsev–Petviashvili equation

Abstract

Abstract In this Letter, Boussinesq–Burgers equation and ( 3 + 1 )-dimensional Kadomtsev–Petviashvili equation are studied by using a generalized algebraic method. A variety of explicit exact travelling wave solutions, including solitary wave, Jacobi and Weierstrass elliptic function periodic, triangular periodic and rational solutions, are obtained. Many new results are presented. The proposed method can be also extended to construct more new exact travelling wave solutions of some nonlinear evolution equations with variable coefficients in mathematical physics.