Similarity reductions and new exact solutions for (3+1)-dimensional B–B equation

The main objective of this investigation is to obtain new closed form solutions for the (3+1)-dimensional Bateman–Burgers equation (B–B equation) by the symmetry method and developed Exp-function method (DEFM). The symmetry method is utilized to infer the infinitesimal generators and build the commutation relations. The similarity reductions of the governing partial differential equations are obtained. The governing partial differential equations are reduced to different ordinary differential equations. The ordinary differential equations are solved by using DEFM. The solutions are analyzed numerically to show the behaviors of the solutions. Solution behaviors include the solitary wave solution, the singular wave solution, the kink wave solution, and the anti-kink wave solution.