Solitary wave solutions of Sawada-Kotera equation using two efficient analytical methods

Muhammad Bilal Riaz; Faiza Naseer; Muhammad Abbas; Magda Abd El-Rahman; Tahir Nazir; Choon Kit Chan; Muhammad Bilal Riaz; Faiza Naseer; Muhammad Abbas; Magda Abd El-Rahman; Tahir Nazir; Choon Kit Chan

doi:10.3934/math.20231601

AIMS Mathematics

2023, Volume 8, Issue 12: 31268-31292. doi: 10.3934/math.20231601

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Solitary wave solutions of Sawada-Kotera equation using two efficient analytical methods

1.
IT4Innovations, VSB–Technical University of Ostrava, Ostrava, Czech Republic
2.
Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
3.
Faculty of Engineering and Quantity Surveying, INTI International University, Putra Nilai, 71800 Negeri Sembilan, Malaysia
4.
Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
5.
Department of Physics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia

Received: 05 September 2023 Revised: 07 December 2023 Accepted: 13 December 2023 Published: 19 December 2023
MSC : 26A48, 26A51, 33B10, 39A1, 39B62

The soliton solutions are one of the stable solutions where nonlinearity and dispersion are perfectly balanced. They are used in a wide variety of physical fields, including plasma, solid state, neuronal, biological production, and diffusion processes. Different analytical methods have been used until now to obtain the soliton solutions of the Sawada-Kotera (SK) equation. The purpose of this study is to offer two successful analytical methods for solving the classical (1+1) dimensional Sawada-Kotera (SK) equation. In order to solve the partial differential equation (PDE), both the modified auxiliary equation method (MAEM) and the extended direct algebraic method are applied. The classical fifth-order SK equation is examined in this study, leading to a variety of precise soliton solutions, including single, periodic, and dark soliton, which are obtained analytically. To illustrate the effect of the parameters, the results are shown in graphical form.
- modified auxiliary equation method,
- Sawada-Kotera equation,
- trigonometric solutions,
- hyperbolic solutions,
- extended direct algebraic method
Citation: Muhammad Bilal Riaz, Faiza Naseer, Muhammad Abbas, Magda Abd El-Rahman, Tahir Nazir, Choon Kit Chan. Solitary wave solutions of Sawada-Kotera equation using two efficient analytical methods[J]. AIMS Mathematics, 2023, 8(12): 31268-31292. doi: 10.3934/math.20231601

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Abstract

The soliton solutions are one of the stable solutions where nonlinearity and dispersion are perfectly balanced. They are used in a wide variety of physical fields, including plasma, solid state, neuronal, biological production, and diffusion processes. Different analytical methods have been used until now to obtain the soliton solutions of the Sawada-Kotera (SK) equation. The purpose of this study is to offer two successful analytical methods for solving the classical (1+1) dimensional Sawada-Kotera (SK) equation. In order to solve the partial differential equation (PDE), both the modified auxiliary equation method (MAEM) and the extended direct algebraic method are applied. The classical fifth-order SK equation is examined in this study, leading to a variety of precise soliton solutions, including single, periodic, and dark soliton, which are obtained analytically. To illustrate the effect of the parameters, the results are shown in graphical form.

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