51. Construction of localized solutions to a generalized (3+1)-dimensional Burgers equation
- Author
-
Wen-Xiu Ma, Rui Zhang, Xiaorui Hu, and Shoufeng Shen
- Subjects
Maple ,Integrable system ,Mathematical analysis ,One-dimensional space ,General Physics and Astronomy ,engineering.material ,01 natural sciences ,010305 fluids & plasmas ,Burgers' equation ,Nonlinear system ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Transformation (function) ,0103 physical sciences ,engineering ,Soliton ,010306 general physics ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematics ,Variable (mathematics) - 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 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-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 Painleve integrable ( N + 1 )-dimensional Burgers equation.
- Published
- 2020