New investigation of the analytical behaviors for some nonlinear PDEs in mathematical physics and modern engineering
Numerous complex situations arising from science and engineering are modeled by integral-differential equations (IDEs). Examples of these situations include mathematical modeling of infectious diseases, epidemics, circuit analysis, voltage drop equations, computational neuroscience, intergalactic mo...
| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818123001213 |
| _version_ | 1797260371123240960 |
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| author | Abdul Hamid Ganie Lamiaa H. Sadek M.M. Tharwat M. Ashik Iqbal M. Mamun Miah Md Mamunur Rasid Nasser S. Elazab M.S. Osman |
| author_facet | Abdul Hamid Ganie Lamiaa H. Sadek M.M. Tharwat M. Ashik Iqbal M. Mamun Miah Md Mamunur Rasid Nasser S. Elazab M.S. Osman |
| author_sort | Abdul Hamid Ganie |
| collection | DOAJ |
| description | Numerous complex situations arising from science and engineering are modeled by integral-differential equations (IDEs). Examples of these situations include mathematical modeling of infectious diseases, epidemics, circuit analysis, voltage drop equations, computational neuroscience, intergalactic modeling, and many more. To explain the mathematical structure and the behavior of various phenomena in nature, two equations with simple mathematical structure namely: the (1 + 1)-dimensional integro-differential Ito equation (IDIE) and the (2 + 1)-dimensional integro-differential Sawada-Kotera equation (IDSKE) are considered. In this analytical investigation, we have conducted an in-depth enquiry to trace the distinctive closed form progressive wave solutions of these proposed models using the (G′G′+G+A)-expansion method. The graphical forms of the acquired solutions have been displayed in the bell-shaped soliton, singular periodic, and anti-kink shape soliton solutions after the values for the free parameters were specified. The two non-algebraic solutions, named, exponential and trigonometric function solutions, have emerged by applying our proposed method. Based on the general findings of our investigation for different parametric values, the attained wave solutions revealed can keep a vital role for natural balances and can be engaged in modern physical applications. The parameters have a visible effect on the wave amplitude and the swiftness of the traveling wave. The executed outcomes are innovative and have monumental applications in the present research, especially in the fields of theoretical physics, astrophysics, plasma physics, particle physics, theory of relativity, advance quantum mechanics, string theory, and geotechnical engineering. |
| first_indexed | 2024-03-08T21:24:36Z |
| format | Article |
| id | doaj.art-d62836e39f8440ad90517d5b1fb94276 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-04-24T23:24:15Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-d62836e39f8440ad90517d5b1fb942762024-03-16T05:09:28ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-03-019100608New investigation of the analytical behaviors for some nonlinear PDEs in mathematical physics and modern engineeringAbdul Hamid Ganie0Lamiaa H. Sadek1M.M. Tharwat2M. Ashik Iqbal3M. Mamun Miah4Md Mamunur Rasid5Nasser S. Elazab6M.S. Osman7Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi ArabiaDepartment of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef 62511, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef 62511, EgyptDepartment of Mathematics & Physics, Khulna Agricultural University, Khulna 9100, BangladeshDepartment of Mathematics, Khulna University of Engineering & Technology, Khulna 9203, Bangladesh; Division of Mathematical and Physical Sciences, Kanazawa University, Kanazawa 9201192, Japan; Corresponding author at: Department of Mathematics, Khulna University of Engineering & Technology, Khulna 9203, Bangladesh.Division of Mathematical and Physical Sciences, Kanazawa University, Kanazawa 9201192, JapanDepartment of Mathematics, Faculty of Sciences, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Sciences, Cairo University, Giza 12613, Egypt; Mathematics Department, Faculty of Applied Sciences, Umm Al-Qura University, Makkah 21955, Saudi ArabiaNumerous complex situations arising from science and engineering are modeled by integral-differential equations (IDEs). Examples of these situations include mathematical modeling of infectious diseases, epidemics, circuit analysis, voltage drop equations, computational neuroscience, intergalactic modeling, and many more. To explain the mathematical structure and the behavior of various phenomena in nature, two equations with simple mathematical structure namely: the (1 + 1)-dimensional integro-differential Ito equation (IDIE) and the (2 + 1)-dimensional integro-differential Sawada-Kotera equation (IDSKE) are considered. In this analytical investigation, we have conducted an in-depth enquiry to trace the distinctive closed form progressive wave solutions of these proposed models using the (G′G′+G+A)-expansion method. The graphical forms of the acquired solutions have been displayed in the bell-shaped soliton, singular periodic, and anti-kink shape soliton solutions after the values for the free parameters were specified. The two non-algebraic solutions, named, exponential and trigonometric function solutions, have emerged by applying our proposed method. Based on the general findings of our investigation for different parametric values, the attained wave solutions revealed can keep a vital role for natural balances and can be engaged in modern physical applications. The parameters have a visible effect on the wave amplitude and the swiftness of the traveling wave. The executed outcomes are innovative and have monumental applications in the present research, especially in the fields of theoretical physics, astrophysics, plasma physics, particle physics, theory of relativity, advance quantum mechanics, string theory, and geotechnical engineering.http://www.sciencedirect.com/science/article/pii/S2666818123001213The (G′/G′ + G + A)-expansion methodThe progressive wave solutionsThe (1+1)-dimensional integro-differential Ito equationThe (2+1)-dimensiopnal integro-differential Sawada-Kotera equationThe closed form solutionsThe soliton solutions |
| spellingShingle | Abdul Hamid Ganie Lamiaa H. Sadek M.M. Tharwat M. Ashik Iqbal M. Mamun Miah Md Mamunur Rasid Nasser S. Elazab M.S. Osman New investigation of the analytical behaviors for some nonlinear PDEs in mathematical physics and modern engineering Partial Differential Equations in Applied Mathematics The (G′/G′ + G + A)-expansion method The progressive wave solutions The (1+1)-dimensional integro-differential Ito equation The (2+1)-dimensiopnal integro-differential Sawada-Kotera equation The closed form solutions The soliton solutions |
| title | New investigation of the analytical behaviors for some nonlinear PDEs in mathematical physics and modern engineering |
| title_full | New investigation of the analytical behaviors for some nonlinear PDEs in mathematical physics and modern engineering |
| title_fullStr | New investigation of the analytical behaviors for some nonlinear PDEs in mathematical physics and modern engineering |
| title_full_unstemmed | New investigation of the analytical behaviors for some nonlinear PDEs in mathematical physics and modern engineering |
| title_short | New investigation of the analytical behaviors for some nonlinear PDEs in mathematical physics and modern engineering |
| title_sort | new investigation of the analytical behaviors for some nonlinear pdes in mathematical physics and modern engineering |
| topic | The (G′/G′ + G + A)-expansion method The progressive wave solutions The (1+1)-dimensional integro-differential Ito equation The (2+1)-dimensiopnal integro-differential Sawada-Kotera equation The closed form solutions The soliton solutions |
| url | http://www.sciencedirect.com/science/article/pii/S2666818123001213 |
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