Abstract
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.
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