Some new exact solutions of \((3+1)\) -dimensional Burgers system via Lie symmetry analysis

Advances in Difference Equations

article

Alimirzaluo, Elnaz¹  Nadjafikhah, Mehdi¹  Manafian, Jalil² 

[1] Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology;Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz

关键词: Analysis burgers equation;    Symmetry group;    Optimal system;    Nonclassical symmetries;    Tanh method;   

DOI  :  10.1186/s13662-021-03220-3

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, by using the Lie symmetry analysis, all of the geometric vector fields of the$(3+1)$ -Burgers system are obtained. We find the 1, 2, and 3-dimensional optimal system of the Burger system and then by applying the 3-dimensional optimal system reduce the order of the system. Also the nonclassical symmetries of the$(3+1)$ -Burgers system will be found by employing nonclassical methods. Finally, the ansatz solutions of BS equations with the aid of the tanh method has been presented. The achieved solutions are investigated through two- and three-dimensional plots for different values of parameters. The analytical simulations are presented to ensure the efficiency of the considered technique. The behavior of the obtained results for multiple cases of symmetries is captured in the present framework. The outcomes of the present investigation show that the considered scheme is efficient and powerful to solve nonlinear differential equations that arise in the sciences and technology.

【 授权许可】

CC BY