Lie symmetries of Benjamin-Ono equation

Weidong Zhao; Mobeen Munir; Ghulam Murtaza; Muhammad Athar; Weidong Zhao; Mobeen Munir; Ghulam Murtaza; Muhammad Athar

doi:10.3934/mbe.2021466

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 9496-9510. doi: 10.3934/mbe.2021466

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Lie symmetries of Benjamin-Ono equation

1.
School of Computer Science, Chengdu University, China
2.
Department of Mathematics, University of Punjab, Lahore, Pakistan
3.
Department of Mathematics, University of Education, Lahore, Pakistan

Received: 28 June 2021 Accepted: 03 September 2021 Published: 29 October 2021

Lie Symmetry analysis is often used to exploit the conservative laws of nature and solve or at least reduce the order of differential equation. One dimension internal waves are best described by Benjamin-Ono equation which is a nonlinear partial integro-differential equation. Present article focuses on the Lie symmetry analysis of this equation because of its importance. Lie symmetry analysis of this equation has been done but there are still some gaps and errors in the recent work. We claim that the symmetry algebra is of five dimensional. We reduce the model and solve it. We give its solution and analyze them graphically.
- Benjamin-Ono equation,
- Lie symmetry,
- one parameter Lie group,
- similarity reduction,
- invariant solutions,
- optimal system
Citation: Weidong Zhao, Mobeen Munir, Ghulam Murtaza, Muhammad Athar. Lie symmetries of Benjamin-Ono equation[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 9496-9510. doi: 10.3934/mbe.2021466

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Abstract

Lie Symmetry analysis is often used to exploit the conservative laws of nature and solve or at least reduce the order of differential equation. One dimension internal waves are best described by Benjamin-Ono equation which is a nonlinear partial integro-differential equation. Present article focuses on the Lie symmetry analysis of this equation because of its importance. Lie symmetry analysis of this equation has been done but there are still some gaps and errors in the recent work. We claim that the symmetry algebra is of five dimensional. We reduce the model and solve it. We give its solution and analyze them graphically.

References

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