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Research Article | Open Access

Traveling wave solutions to the Boussinesq equation via Sardar sub-equation technique

Hamood-Ur-Rahman1, Muhammad Imran Asjad2, Nayab Munawar1, Foroud parvaneh3, Taseer Muhammad4, Ahmed A. Hamoud5, Homan Emadifar6,7( ), Faraidun K. Hamasalh7, Hooshmand Azizi8, Masoumeh Khademi6
Department of Mathematics, University Of Okara, Okara, Pakistan
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
Department of Mathematics, Taiz University, Taiz-380 015, Yemen
Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran
Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Iraq
Department of Electrical and Computer Engineering, No.1 Faculty of Kermanshah, Technical and Vocational University (TVU), Kermanshah, Iran
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Abstract

In present study, the Boussinesq equation is obtained by means of the Sardar Sub-Equation Technique (SSET) to create unique soliton solutions containing parameters. Using this technique, different solutions are obtained, such as the singular soliton, the dark-bright soliton, the bright soliton and the periodic soliton. The graphs of these solutions are plotted for a batter understanding of the model. The results show that the technique is very effective in solving nonlinear partial differential equations (PDEs) arising in mathematical physics.

Keywords

Boussinesq equationSardar sub-equation methodtraveling wave soliton solutions
CLC number: 32W50, 35C08, 35C15

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 11134-11149
DOI: 10.3934/math.2022623

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Hamood-Ur-Rahman, Asjad MI, Munawar N, et al. Traveling wave solutions to the Boussinesq equation via Sardar sub-equation technique. AIMS Mathematics, 2022, 7(6): 11134-11149. https://doi.org/10.3934/math.2022623

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Received: 07 December 2021
Revised: 26 February 2022
Accepted: 28 February 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)