Abstract
•Variable separation solutions are constructed.•The lump (not lump-type) solutions are derived.•Interactions between the lump and N-solitons are investigated.•Interactions between the lump and other traveling waves are discussed.•All the resulting solutions can be generalized to (N+1)-dimensional Burgers equation.
Finding exact and analytic solutions of nonlinear system in high dimensions is a difficult but meaningful work. In this paper, by means of the symbolic package Maple, we investigate a Painlevé integrable (3+1)-dimensional generalized Burgers (gBurgers) equation. Starting from the Cole-Hopf transformation with different seed solutions, abundant localized solutions are provided, including new variable separation solutions, lumps, lump-“multiple-soliton” solutions and other interaction solutions. Specifically, the lump-two soliton solution and lump-soliton-periodic solution are depicted by the three-dimensional plots and contour plots at different times, respectively. The methods and all the resulting solutions presented in this paper can be generalized to the Painlevé integrable (N+1)-dimensional Burgers equation.