Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach
The (3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation, dynamics of shallow water wave, plasma fluid model, chemical kinematics, chemical engin...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-06-01
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| Series: | Journal of Ocean Engineering and Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468013321000772 |
| _version_ | 1811326616439095296 |
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| author | Md. Rezwan Ahamed Fahim Purobi Rani Kundu Md. Ekramul Islam M. Ali Akbar M.S. Osman |
| author_facet | Md. Rezwan Ahamed Fahim Purobi Rani Kundu Md. Ekramul Islam M. Ali Akbar M.S. Osman |
| author_sort | Md. Rezwan Ahamed Fahim |
| collection | DOAJ |
| description | The (3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation, dynamics of shallow water wave, plasma fluid model, chemical kinematics, chemical engineering, geochemistry, and many other topics. In this article, we have assessed the effects of wave speed and physical parameters on the wave contours and confirmed that waveform changes with the variety of the free factors in it. As a result, wave solutions are extensively analyzed by using the balancing condition on the linear and nonlinear terms of the highest order and extracted different standard wave configurations, containing kink, breather soliton, bell-shaped soliton, and periodic waves. To extract the soliton solutions of the high-dimensional nonlinear evolution equations, a recently developed approach of the sine-Gordon expansion method is used to derive the wave solutions directly. The sine-Gordon expansion approach is a potent and strategic mathematical tool for instituting ample of new traveling wave solutions of nonlinear equations. This study established the efficiency of the described method in solving evolution equations which are nonlinear and with higher dimension (HNEEs). Closed-form solutions are carefully illustrated and discussed through diagrams. |
| first_indexed | 2024-04-13T14:52:06Z |
| format | Article |
| id | doaj.art-f9c258e0fc064a5682ffe5b2e4a0db85 |
| institution | Directory Open Access Journal |
| issn | 2468-0133 |
| language | English |
| last_indexed | 2024-04-13T14:52:06Z |
| publishDate | 2022-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Ocean Engineering and Science |
| spelling | doaj.art-f9c258e0fc064a5682ffe5b2e4a0db852022-12-22T02:42:34ZengElsevierJournal of Ocean Engineering and Science2468-01332022-06-0173272279Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approachMd. Rezwan Ahamed Fahim0Purobi Rani Kundu1Md. Ekramul Islam2M. Ali Akbar3M.S. Osman4Department of Mathematics, Pabna University of Science and Technology, BangladeshDepartment of Mathematics, Pabna University of Science and Technology, BangladeshDepartment of Mathematics, Pabna University of Science and Technology, BangladeshDepartment of Applied Mathematics, University of Rajshahi, BangladeshDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt; Department of Mathematics, Faculty of Applied Science, Umm Alqura University, Makkah 21955, Saudi Arabia; Corresponding author.The (3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation, dynamics of shallow water wave, plasma fluid model, chemical kinematics, chemical engineering, geochemistry, and many other topics. In this article, we have assessed the effects of wave speed and physical parameters on the wave contours and confirmed that waveform changes with the variety of the free factors in it. As a result, wave solutions are extensively analyzed by using the balancing condition on the linear and nonlinear terms of the highest order and extracted different standard wave configurations, containing kink, breather soliton, bell-shaped soliton, and periodic waves. To extract the soliton solutions of the high-dimensional nonlinear evolution equations, a recently developed approach of the sine-Gordon expansion method is used to derive the wave solutions directly. The sine-Gordon expansion approach is a potent and strategic mathematical tool for instituting ample of new traveling wave solutions of nonlinear equations. This study established the efficiency of the described method in solving evolution equations which are nonlinear and with higher dimension (HNEEs). Closed-form solutions are carefully illustrated and discussed through diagrams.http://www.sciencedirect.com/science/article/pii/S2468013321000772Sine-Gordon expansion approachKadomtsev-Petviashvili equationmodified KdV-Zakharov-Kuznetsov equationsoliton solutions |
| spellingShingle | Md. Rezwan Ahamed Fahim Purobi Rani Kundu Md. Ekramul Islam M. Ali Akbar M.S. Osman Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach Journal of Ocean Engineering and Science Sine-Gordon expansion approach Kadomtsev-Petviashvili equation modified KdV-Zakharov-Kuznetsov equation soliton solutions |
| title | Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach |
| title_full | Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach |
| title_fullStr | Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach |
| title_full_unstemmed | Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach |
| title_short | Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach |
| title_sort | wave profile analysis of a couple of 3 1 dimensional nonlinear evolution equations by sine gordon expansion approach |
| topic | Sine-Gordon expansion approach Kadomtsev-Petviashvili equation modified KdV-Zakharov-Kuznetsov equation soliton solutions |
| url | http://www.sciencedirect.com/science/article/pii/S2468013321000772 |
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