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

Hamood-Ur-Rahman; Muhammad Imran Asjad; Nayab Munawar; Foroud parvaneh; Taseer Muhammad; Ahmed A. Hamoud; Homan Emadifar; Faraidun K. Hamasalh; Hooshmand Azizi; Masoumeh Khademi; Hamood-Ur-Rahman; Muhammad Imran Asjad; Nayab Munawar; Foroud parvaneh; Taseer Muhammad; Ahmed A. Hamoud; Homan Emadifar; Faraidun K. Hamasalh; Hooshmand Azizi; Masoumeh Khademi

doi:10.3934/math.2022623

AIMS Mathematics

2022, Volume 7, Issue 6: 11134-11149. doi: 10.3934/math.2022623

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Research article

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

1.
Department of Mathematics, University Of Okara, Okara, Pakistan
2.
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
3.
Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
4.
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
5.
Department of Mathematics, Taiz University, Taiz-380 015, Yemen
6.
Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran
7.
Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Iraq
8.
Department of Electrical and Computer Engineering, No.1 Faculty of Kermanshah, Technical and Vocational University (TVU), Kermanshah, Iran

Received: 07 December 2021 Revised: 26 February 2022 Accepted: 28 February 2022 Published: 08 April 2022
MSC : 32W50, 35C08, 35C15

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.
- Boussinesq equation,
- Sardar sub-equation method,
- traveling wave soliton solutions
Citation: Hamood-Ur-Rahman, Muhammad Imran Asjad, Nayab Munawar, Foroud parvaneh, Taseer Muhammad, Ahmed A. Hamoud, Homan Emadifar, Faraidun K. Hamasalh, Hooshmand Azizi, Masoumeh Khademi. Traveling wave solutions to the Boussinesq equation via Sardar sub-equation technique[J]. AIMS Mathematics, 2022, 7(6): 11134-11149. doi: 10.3934/math.2022623

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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.

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