Rational solutions and some interactions phenomena of a (3+1)-dimensional BLMP equation in incompressible fluids: A Hirota bilinear method and dimensionally reduction approach
This manuscript addresses the rational solutions of a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation, emphasizing key aspects in response to specific questions. The study begins by elucidating the problem’s significance, highlighting the pursuit of rational solutions for the mentioned...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-01-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723010628 |
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| author | Mati ur Rahman Mohammad Alqudah Meraj Ali Khan Bent Elmina Haroun Ali Shabir Ahmad Emad E. Mahmoud Mei Sun |
| author_facet | Mati ur Rahman Mohammad Alqudah Meraj Ali Khan Bent Elmina Haroun Ali Shabir Ahmad Emad E. Mahmoud Mei Sun |
| author_sort | Mati ur Rahman |
| collection | DOAJ |
| description | This manuscript addresses the rational solutions of a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation, emphasizing key aspects in response to specific questions. The study begins by elucidating the problem’s significance, highlighting the pursuit of rational solutions for the mentioned equation. The methodology involves obtaining the Hirota bilinear (HB) form through a transformative process. Furthermore, the analysis extends to the dimensionally reduced BLMP equation, specifically exploring lump and rogue wave-like (Rwl) solutions, along with the interaction between kink and lump solutions. The HB forms play a crucial role in this examination. Importantly, the solutions presented in this study are characterized as non-singular and localized. Visualizations of these solutions are instrumental in understanding the equation’s behavior, particularly how the solutions evolve under varying physical conditions. The outcomes are visually conveyed through 3D and surface graphs, offering a comprehensive representation for specific parameter values. In conclusion, this work contributes novel insights beyond previous efforts in the literature, showcasing the importance and advancements in the study of the (3+1)-dimensional BLMP equation. |
| first_indexed | 2024-03-08T12:52:56Z |
| format | Article |
| id | doaj.art-fc694b71db7742fa9558d4c55691227f |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-08T12:52:56Z |
| publishDate | 2024-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-fc694b71db7742fa9558d4c55691227f2024-01-20T04:45:12ZengElsevierResults in Physics2211-37972024-01-0156107269Rational solutions and some interactions phenomena of a (3+1)-dimensional BLMP equation in incompressible fluids: A Hirota bilinear method and dimensionally reduction approachMati ur Rahman0Mohammad Alqudah1Meraj Ali Khan2Bent Elmina Haroun Ali3Shabir Ahmad4Emad E. Mahmoud5Mei Sun6School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, PR China; Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut 11022801, LebanonSchool of Basic Sciences and Humanities, German Jordanian University, Amman, 11180, JordanDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU) P.O. Box-65892, Riyadh 11566, Saudi ArabiaDepartment of Mathematics, College of Science and Arts Qassim University, Riyadh, Alkhbra, Saudi Arabia; Sinar University- Faculty Of Education Department Of Physics and Mathematics, Sinja, Republic of the SudanDepartment of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pukhtunkhwa, PakistanDepartment of Mathematics and Statistics, College of Science, Taif University, PO Box 11099, Taif 21944, Saudi ArabiaSchool of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, PR China; Corresponding author.This manuscript addresses the rational solutions of a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation, emphasizing key aspects in response to specific questions. The study begins by elucidating the problem’s significance, highlighting the pursuit of rational solutions for the mentioned equation. The methodology involves obtaining the Hirota bilinear (HB) form through a transformative process. Furthermore, the analysis extends to the dimensionally reduced BLMP equation, specifically exploring lump and rogue wave-like (Rwl) solutions, along with the interaction between kink and lump solutions. The HB forms play a crucial role in this examination. Importantly, the solutions presented in this study are characterized as non-singular and localized. Visualizations of these solutions are instrumental in understanding the equation’s behavior, particularly how the solutions evolve under varying physical conditions. The outcomes are visually conveyed through 3D and surface graphs, offering a comprehensive representation for specific parameter values. In conclusion, this work contributes novel insights beyond previous efforts in the literature, showcasing the importance and advancements in the study of the (3+1)-dimensional BLMP equation.http://www.sciencedirect.com/science/article/pii/S2211379723010628Hirota methodRational solutionsBilinear formRogue waves |
| spellingShingle | Mati ur Rahman Mohammad Alqudah Meraj Ali Khan Bent Elmina Haroun Ali Shabir Ahmad Emad E. Mahmoud Mei Sun Rational solutions and some interactions phenomena of a (3+1)-dimensional BLMP equation in incompressible fluids: A Hirota bilinear method and dimensionally reduction approach Results in Physics Hirota method Rational solutions Bilinear form Rogue waves |
| title | Rational solutions and some interactions phenomena of a (3+1)-dimensional BLMP equation in incompressible fluids: A Hirota bilinear method and dimensionally reduction approach |
| title_full | Rational solutions and some interactions phenomena of a (3+1)-dimensional BLMP equation in incompressible fluids: A Hirota bilinear method and dimensionally reduction approach |
| title_fullStr | Rational solutions and some interactions phenomena of a (3+1)-dimensional BLMP equation in incompressible fluids: A Hirota bilinear method and dimensionally reduction approach |
| title_full_unstemmed | Rational solutions and some interactions phenomena of a (3+1)-dimensional BLMP equation in incompressible fluids: A Hirota bilinear method and dimensionally reduction approach |
| title_short | Rational solutions and some interactions phenomena of a (3+1)-dimensional BLMP equation in incompressible fluids: A Hirota bilinear method and dimensionally reduction approach |
| title_sort | rational solutions and some interactions phenomena of a 3 1 dimensional blmp equation in incompressible fluids a hirota bilinear method and dimensionally reduction approach |
| topic | Hirota method Rational solutions Bilinear form Rogue waves |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723010628 |
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