Theoretical examination and simulations of two nonlinear evolution equations along with stability analysis
Nonlinear evolution equations are employed in the representation of diverse intricate physical events, and the identification of precise solutions for these equations holds significance about their practical implementations. One of the significant challenges is the identification of traveling wave s...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379724001864 |
| _version_ | 1797259978088644608 |
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| author | Muhammad Abdaal Bin Iqbal Ejaz Hussain Syed Asif Ali Shah Zhao Li Muhammd Zubair Raza Adham E. Ragab Emad A. Az-Zo’bi Mohamed R. Ali |
| author_facet | Muhammad Abdaal Bin Iqbal Ejaz Hussain Syed Asif Ali Shah Zhao Li Muhammd Zubair Raza Adham E. Ragab Emad A. Az-Zo’bi Mohamed R. Ali |
| author_sort | Muhammad Abdaal Bin Iqbal |
| collection | DOAJ |
| description | Nonlinear evolution equations are employed in the representation of diverse intricate physical events, and the identification of precise solutions for these equations holds significance about their practical implementations. One of the significant challenges is the identification of traveling wave solutions inside established nonlinear evolution systems in the field of mathematical physics. In the present research, we employ the modified sub-equation approach, a very effective and strong technique, to ensure the solutions for the Klein–Gordon featuring cubic nonlinearity and Zakharov Kuznetsov–Benjamin Bona Mahony equations. Several restriction requirements that ensure the existence of these solutions are emphasized. By employing a linearization technique, we ascertain the stability gain. This methodology acquires original precise solutions of soliton nature. Furthermore, the nonlinear wave structures of both equations are illustrated through the consideration of several three-dimensional and two-dimensional plots. These plots are generated by selecting appropriate values for the parameters. It is expected that these innovative solutions would facilitate an in-depth understanding of the evolution and fluidity of these models. The solutions obtained comprise periodic functions, mixed periodic functions, rational solutions, and exponential solutions. |
| first_indexed | 2024-03-07T18:35:53Z |
| format | Article |
| id | doaj.art-11aec1a30bb646eb8af91f3d797632d0 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-24T23:18:00Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-11aec1a30bb646eb8af91f3d797632d02024-03-17T07:53:43ZengElsevierResults in Physics2211-37972024-03-0158107504Theoretical examination and simulations of two nonlinear evolution equations along with stability analysisMuhammad Abdaal Bin Iqbal0Ejaz Hussain1Syed Asif Ali Shah2Zhao Li3Muhammd Zubair Raza4Adham E. Ragab5Emad A. Az-Zo’bi6Mohamed R. Ali7Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, PakistanDepartment of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, PakistanDepartment of Mathematics and Statistics, The University of Lahore, 1-km Defence Road, Lahore 54000, PakistanCollege of Computer Science, Chengdu University, Chengdu, 610106, PR ChinaDepartment of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, PakistanDepartment of Industrial Engineering, College of Engineering King Saud University, P.O. Box 800, Riyadh 11421, Saudi ArabiaDepartment of Mathematics, Mutah University, Mutah, Al Karak, JordanFaculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835, Egypt; Basic Engineering Science Department, Benha Faculty of Engineering, Benha University, Benha, Egypt; Corresponding author.Nonlinear evolution equations are employed in the representation of diverse intricate physical events, and the identification of precise solutions for these equations holds significance about their practical implementations. One of the significant challenges is the identification of traveling wave solutions inside established nonlinear evolution systems in the field of mathematical physics. In the present research, we employ the modified sub-equation approach, a very effective and strong technique, to ensure the solutions for the Klein–Gordon featuring cubic nonlinearity and Zakharov Kuznetsov–Benjamin Bona Mahony equations. Several restriction requirements that ensure the existence of these solutions are emphasized. By employing a linearization technique, we ascertain the stability gain. This methodology acquires original precise solutions of soliton nature. Furthermore, the nonlinear wave structures of both equations are illustrated through the consideration of several three-dimensional and two-dimensional plots. These plots are generated by selecting appropriate values for the parameters. It is expected that these innovative solutions would facilitate an in-depth understanding of the evolution and fluidity of these models. The solutions obtained comprise periodic functions, mixed periodic functions, rational solutions, and exponential solutions.http://www.sciencedirect.com/science/article/pii/S2211379724001864(1+1).dimensional Klein–Gordon equationZakharov–Kuznetsov Benjamin–Bona MahonyModified sub-equation methodStability analysisExact solution |
| spellingShingle | Muhammad Abdaal Bin Iqbal Ejaz Hussain Syed Asif Ali Shah Zhao Li Muhammd Zubair Raza Adham E. Ragab Emad A. Az-Zo’bi Mohamed R. Ali Theoretical examination and simulations of two nonlinear evolution equations along with stability analysis Results in Physics (1+1).dimensional Klein–Gordon equation Zakharov–Kuznetsov Benjamin–Bona Mahony Modified sub-equation method Stability analysis Exact solution |
| title | Theoretical examination and simulations of two nonlinear evolution equations along with stability analysis |
| title_full | Theoretical examination and simulations of two nonlinear evolution equations along with stability analysis |
| title_fullStr | Theoretical examination and simulations of two nonlinear evolution equations along with stability analysis |
| title_full_unstemmed | Theoretical examination and simulations of two nonlinear evolution equations along with stability analysis |
| title_short | Theoretical examination and simulations of two nonlinear evolution equations along with stability analysis |
| title_sort | theoretical examination and simulations of two nonlinear evolution equations along with stability analysis |
| topic | (1+1).dimensional Klein–Gordon equation Zakharov–Kuznetsov Benjamin–Bona Mahony Modified sub-equation method Stability analysis Exact solution |
| url | http://www.sciencedirect.com/science/article/pii/S2211379724001864 |
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