Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches
In this paper, we analyze and provide innovative soliton solutions for a (2+1)-dimensional generalized Korteweg-de Vries (gKdV) problem. We obtain phase shifts and dispersion relations by using the generalized Arnous technique and the Riccati equation approach, thus allowing different soliton soluti...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241664 |
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| author | Ibrahim Alraddadi Faisal Alsharif Sandeep Malik Hijaz Ahmad Taha Radwan Karim K. Ahmed |
| author_facet | Ibrahim Alraddadi Faisal Alsharif Sandeep Malik Hijaz Ahmad Taha Radwan Karim K. Ahmed |
| author_sort | Ibrahim Alraddadi |
| collection | DOAJ |
| description | In this paper, we analyze and provide innovative soliton solutions for a (2+1)-dimensional generalized Korteweg-de Vries (gKdV) problem. We obtain phase shifts and dispersion relations by using the generalized Arnous technique and the Riccati equation approach, thus allowing different soliton solutions to be developed. Several precise solutions with special structural properties, including kink and solitary soliton solutions, are included in our study. This detailed examination demonstrates the complex behavior of the model and its capability to explain a large scale of nonlinear wave occurrences in many physical settings. Thus, in scientific domains such as fluid mechanics, plasma physics, and wave propagation in media ranging from ocean surfaces to optical fibers, our results are crucial to comprehend the principles behind the production and propagation of many complicated phenomena. Finally, we provide 2D and 3D graphs for various solutions that have been obtained using Maple. |
| format | Article |
| id | doaj-art-811ea95515124e26a03418eea58c62a4 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-811ea95515124e26a03418eea58c62a42025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912349663498010.3934/math.20241664Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approachesIbrahim Alraddadi0Faisal Alsharif1Sandeep Malik2Hijaz Ahmad3Taha Radwan4Karim K. Ahmed5Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi ArabiaDepartment of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi ArabiaDepartment of Mathematics, Akal University, Talwandi Sabo, Bathinda, Punjab, 151302, IndiaDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi ArabiaDepartment of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, EgyptIn this paper, we analyze and provide innovative soliton solutions for a (2+1)-dimensional generalized Korteweg-de Vries (gKdV) problem. We obtain phase shifts and dispersion relations by using the generalized Arnous technique and the Riccati equation approach, thus allowing different soliton solutions to be developed. Several precise solutions with special structural properties, including kink and solitary soliton solutions, are included in our study. This detailed examination demonstrates the complex behavior of the model and its capability to explain a large scale of nonlinear wave occurrences in many physical settings. Thus, in scientific domains such as fluid mechanics, plasma physics, and wave propagation in media ranging from ocean surfaces to optical fibers, our results are crucial to comprehend the principles behind the production and propagation of many complicated phenomena. Finally, we provide 2D and 3D graphs for various solutions that have been obtained using Maple.https://www.aimspress.com/article/doi/10.3934/math.20241664mathematical modelanalytic solutionssoliton solutionsgeneralized kdv equationgeneralized arnous methodriccati equation method |
| spellingShingle | Ibrahim Alraddadi Faisal Alsharif Sandeep Malik Hijaz Ahmad Taha Radwan Karim K. Ahmed Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches AIMS Mathematics mathematical model analytic solutions soliton solutions generalized kdv equation generalized arnous method riccati equation method |
| title | Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches |
| title_full | Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches |
| title_fullStr | Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches |
| title_full_unstemmed | Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches |
| title_short | Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches |
| title_sort | innovative soliton solutions for a 2 1 dimensional generalized kdv equation using two effective approaches |
| topic | mathematical model analytic solutions soliton solutions generalized kdv equation generalized arnous method riccati equation method |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241664 |
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