Construction of localized solutions to a generalized (3+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 Painleve 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-solitonperiodic 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 Painleve integrable (N + 1)-dimensional Burgers equation.