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

Elnaz Alimirzaluo,Mehdi Nadjafikhah,Jalil Manafian

doi:10.1186/s13662-021-03220-3

Elnaz Alimirzaluo, Mehdi Nadjafikhah + Show 1 more

Open Access

https://doi.org/10.1186/s13662-021-03220-3

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Abstract

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.

Highlights

1 Introduction The Burgers system describes the propagation processes for nonlinear waves in fluid mechanics such as diverse non-equilibrium, nonlinear phenomena in turbulence, and interface dynamics [12]. This system is used in solitary wave theory to expand integrable models with the extending of famous physical equations
One of the Sophus Lie’s significant discoveries in differential equation is to indicate that transforming nonlinear conditions is possible by through infinitesimal invariants which can correspond to the generators of the symmetry group of the system [28]
Having the symmetry group of a system of differential equations has many advantages including the ability to classify the solutions of the differential equations system

Summary

Introduction

The Burgers system describes the propagation processes for nonlinear waves in fluid mechanics such as diverse non-equilibrium, nonlinear phenomena in turbulence, and interface dynamics [12]. Using the method of Lie symmetry group a solution will be presented for reduced equations.

Results

Conclusion