A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach
Abstract The space–time fractional nonlinear Klein-Gordon and modified regularized long-wave equations explain the dynamics of spinless ions and relativistic electrons in atom theory, long-wave dynamics in the ocean, like tsunamis and tidal waves, shallow water waves in coastal sea areas, and also m...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-11-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-45423-6 |
| _version_ | 1797452998480232448 |
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| author | Anamika Podder Mohammad Asif Arefin M. Ali Akbar M. Hafiz Uddin |
| author_facet | Anamika Podder Mohammad Asif Arefin M. Ali Akbar M. Hafiz Uddin |
| author_sort | Anamika Podder |
| collection | DOAJ |
| description | Abstract The space–time fractional nonlinear Klein-Gordon and modified regularized long-wave equations explain the dynamics of spinless ions and relativistic electrons in atom theory, long-wave dynamics in the ocean, like tsunamis and tidal waves, shallow water waves in coastal sea areas, and also modeling several nonlinear optical phenomena. In this study, the improved Bernoulli sub-equation function method has been used to generate some new and more universal closed-form traveling wave solutions of those equations in the sense of beta-derivative. Using the fractional complex wave transformation, the equations are converted into nonlinear differential equations. The achieved outcomes are further inclusive of successfully dealing with the aforementioned models. Some projecting solitons waveforms, including, kink, singular soliton, bell shape, anti-bell shape, and other types of solutions are displayed through a three-dimensional plotline, a plot of contour, and a 2D plot for definite parametric values. It is significant to note that all obtained solutions are verified as accurate by substituting the original equation in each case using the computational software, Maple. Additionally, the results have been compared with other existing results in the literature to show their uniqueness. The proposed technique is effective, computationally attractive, and trustworthy to establish more generalized wave solutions. |
| first_indexed | 2024-03-09T15:16:30Z |
| format | Article |
| id | doaj.art-548c9d9c1d324d31b7e85de2a08602b6 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-09T15:16:30Z |
| publishDate | 2023-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-548c9d9c1d324d31b7e85de2a08602b62023-11-26T13:03:20ZengNature PortfolioScientific Reports2045-23222023-11-0113111510.1038/s41598-023-45423-6A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approachAnamika Podder0Mohammad Asif Arefin1M. Ali Akbar2M. Hafiz Uddin3Department of Mathematics, Jashore University of Science and TechnologyDepartment of Mathematics, Jashore University of Science and TechnologyDepartment of Applied Mathematics, University of RajshahiDepartment of Mathematics, Jashore University of Science and TechnologyAbstract The space–time fractional nonlinear Klein-Gordon and modified regularized long-wave equations explain the dynamics of spinless ions and relativistic electrons in atom theory, long-wave dynamics in the ocean, like tsunamis and tidal waves, shallow water waves in coastal sea areas, and also modeling several nonlinear optical phenomena. In this study, the improved Bernoulli sub-equation function method has been used to generate some new and more universal closed-form traveling wave solutions of those equations in the sense of beta-derivative. Using the fractional complex wave transformation, the equations are converted into nonlinear differential equations. The achieved outcomes are further inclusive of successfully dealing with the aforementioned models. Some projecting solitons waveforms, including, kink, singular soliton, bell shape, anti-bell shape, and other types of solutions are displayed through a three-dimensional plotline, a plot of contour, and a 2D plot for definite parametric values. It is significant to note that all obtained solutions are verified as accurate by substituting the original equation in each case using the computational software, Maple. Additionally, the results have been compared with other existing results in the literature to show their uniqueness. The proposed technique is effective, computationally attractive, and trustworthy to establish more generalized wave solutions.https://doi.org/10.1038/s41598-023-45423-6 |
| spellingShingle | Anamika Podder Mohammad Asif Arefin M. Ali Akbar M. Hafiz Uddin A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach Scientific Reports |
| title | A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach |
| title_full | A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach |
| title_fullStr | A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach |
| title_full_unstemmed | A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach |
| title_short | A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach |
| title_sort | study of the wave dynamics of the space time fractional nonlinear evolution equations of beta derivative using the improved bernoulli sub equation function approach |
| url | https://doi.org/10.1038/s41598-023-45423-6 |
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