Lie symmetries of Generalized Equal Width wave equations

Mobeen Munir; Muhammad Athar; Sakhi Sarwar; Wasfi Shatanawi; Mobeen Munir; Muhammad Athar; Sakhi Sarwar; Wasfi Shatanawi

doi:10.3934/math.2021705

AIMS Mathematics

2021, Volume 6, Issue 11: 12148-12165. doi: 10.3934/math.2021705

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Lie symmetries of Generalized Equal Width wave equations

1.
Department of Mathematics, University of the Punjab, New Campus Lahore, University of the Punjab, Lahore 54590, Pakistan
2.
Department of Mathematics, University of Education, Lahore, Pakistan
3.
Department of Mathematics and General Courses, Prince Sultan University, Riyadh, Saudi Arabia
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 9 40402, Taiwan
5.
Department of Mathematics, Hashemite University, Zarqa, Jordan

Received: 18 June 2021 Accepted: 03 August 2021 Published: 23 August 2021
MSC : 22E70, 34A05, 35A30, 58J70, 58J72

Lie symmetry analysis of differential equations proves to be a powerful tool to solve or atleast to reduce the order and non-linearity of the equation. The present article focuses on the solution of Generalized Equal Width wave (GEW) equation using Lie group theory. Over the years, different solution methods have been tried for GEW but Lie symmetry analysis has not been done yet. At first, we obtain the infinitesimal generators, commutation table and adjoint table of Generalized Equal Width wave (GEW) equation. After this, we find the one dimensional optimal system. Then we reduce GEW equation into non-linear ordinary differential equation (ODE) by using the Lie symmetry method. This transformed equation can take us to the solution of GEW equation by different methods. After this, we get the travelling wave solution of GEW equation by using the Sine-cosine method. We also give graphs of some solutions of this equation.
- Generalized Equal Width wave equation,
- Lie symmetry,
- optimal system,
- reduction,
- travelling wave solution,
- Sine-cosine method
Citation: Mobeen Munir, Muhammad Athar, Sakhi Sarwar, Wasfi Shatanawi. Lie symmetries of Generalized Equal Width wave equations[J]. AIMS Mathematics, 2021, 6(11): 12148-12165. doi: 10.3934/math.2021705

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Abstract

Lie symmetry analysis of differential equations proves to be a powerful tool to solve or atleast to reduce the order and non-linearity of the equation. The present article focuses on the solution of Generalized Equal Width wave (GEW) equation using Lie group theory. Over the years, different solution methods have been tried for GEW but Lie symmetry analysis has not been done yet. At first, we obtain the infinitesimal generators, commutation table and adjoint table of Generalized Equal Width wave (GEW) equation. After this, we find the one dimensional optimal system. Then we reduce GEW equation into non-linear ordinary differential equation (ODE) by using the Lie symmetry method. This transformed equation can take us to the solution of GEW equation by different methods. After this, we get the travelling wave solution of GEW equation by using the Sine-cosine method. We also give graphs of some solutions of this equation.

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