Symmetry solutions and conservation laws of a new generalized 2D Bogoyavlensky-Konopelchenko equation of plasma physics

Chaudry Masood Khalique; Oke Davies Adeyemo; Kentse Maefo; Chaudry Masood Khalique; Oke Davies Adeyemo; Kentse Maefo

doi:10.3934/math.2022544

AIMS Mathematics

2022, Volume 7, Issue 6: 9767-9788. doi: 10.3934/math.2022544

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Symmetry solutions and conservation laws of a new generalized 2D Bogoyavlensky-Konopelchenko equation of plasma physics

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, Republic of South Africa

Received: 03 December 2021 Revised: 05 February 2022 Accepted: 13 February 2022 Published: 17 March 2022
MSC : 35L65, 35B06

In physics as well as mathematics, nonlinear partial differential equations are known as veritable tools in describing many diverse physical systems, ranging from gravitation, mechanics, fluid dynamics to plasma physics. In consequence, we analytically examine a two-dimensional generalized Bogoyavlensky-Konopelchenko equation in plasma physics in this paper. Firstly, the technique of Lie symmetry analysis of differential equations is used to find its symmetries and perform symmetry reductions to obtain ordinary differential equations which are solved to secure possible analytic solutions of the underlying equation. Then we use Kudryashov's and $ (G'/G) $-expansion methods to acquire analytic solutions of the equation. As a result, solutions found in the process include exponential, elliptic, algebraic, hyperbolic and trigonometric functions which are highly important due to their various applications in mathematic and theoretical physics. Moreover, the obtained solutions are represented in diagrams. Conclusively, we construct conservation laws of the underlying equation through the use of multiplier approach. We state here that the results secured for the equation understudy are new and highly useful.
- two-dimensional generalized Bogoyavlensky-Konopelchenko equation,
- Lie point symmetries,
- analytic solutions,
- conservation laws
Citation: Chaudry Masood Khalique, Oke Davies Adeyemo, Kentse Maefo. Symmetry solutions and conservation laws of a new generalized 2D Bogoyavlensky-Konopelchenko equation of plasma physics[J]. AIMS Mathematics, 2022, 7(6): 9767-9788. doi: 10.3934/math.2022544

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Abstract

In physics as well as mathematics, nonlinear partial differential equations are known as veritable tools in describing many diverse physical systems, ranging from gravitation, mechanics, fluid dynamics to plasma physics. In consequence, we analytically examine a two-dimensional generalized Bogoyavlensky-Konopelchenko equation in plasma physics in this paper. Firstly, the technique of Lie symmetry analysis of differential equations is used to find its symmetries and perform symmetry reductions to obtain ordinary differential equations which are solved to secure possible analytic solutions of the underlying equation. Then we use Kudryashov's and $ (G'/G) $-expansion methods to acquire analytic solutions of the equation. As a result, solutions found in the process include exponential, elliptic, algebraic, hyperbolic and trigonometric functions which are highly important due to their various applications in mathematic and theoretical physics. Moreover, the obtained solutions are represented in diagrams. Conclusively, we construct conservation laws of the underlying equation through the use of multiplier approach. We state here that the results secured for the equation understudy are new and highly useful.

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