Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation
In this research, we systematically examined the special solutions of the (3+1)-dimensional evolution equation corresponding to nonclassical symmetries. By employing the identified symmetries, we developed invariant solutions that reveal the underlying structure of the equation and its solutions. Ad...
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| Language: | English |
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Elsevier
2025-01-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447924005574 |
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| author | Ibtehal Alazman Manvendra Narayan Mishra Badr Saad T. Alkahtani Mati ur Rahman |
| author_facet | Ibtehal Alazman Manvendra Narayan Mishra Badr Saad T. Alkahtani Mati ur Rahman |
| author_sort | Ibtehal Alazman |
| collection | DOAJ |
| description | In this research, we systematically examined the special solutions of the (3+1)-dimensional evolution equation corresponding to nonclassical symmetries. By employing the identified symmetries, we developed invariant solutions that reveal the underlying structure of the equation and its solutions. Additionally, bifurcation analysis was conducted to understand the qualitative shifts in the system's behavior. We investigated sensitivity to initial conditions and the presence of unusual attractors to better comprehend the system's chaotic dynamics. While invariant solutions provide exact representations of certain dynamical states, bifurcation and chaos analyses offer insights into the system's intrinsic transitions and complexity. This study not only enhances the theoretical understanding of high-dimensional nonlinear evolution equations but also provides a foundation for future applications in various fields where complex processes are modeled by such equations. |
| format | Article |
| id | doaj-art-d7dd37a960f141c7a1d6d3ff9e427575 |
| institution | Kabale University |
| issn | 2090-4479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj-art-d7dd37a960f141c7a1d6d3ff9e4275752025-01-17T04:49:18ZengElsevierAin Shams Engineering Journal2090-44792025-01-01161103176Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equationIbtehal Alazman0Manvendra Narayan Mishra1Badr Saad T. Alkahtani2Mati ur Rahman3Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi ArabiaDepartment of Mathematics, Suresh Gyan Vihar University, Rajasthan IndiaDepartment of Mathematics, College of Science, King Saud University, Riyadh 11989, Saudi ArabiaSchool of Mathematics Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu PR China; Corresponding author.In this research, we systematically examined the special solutions of the (3+1)-dimensional evolution equation corresponding to nonclassical symmetries. By employing the identified symmetries, we developed invariant solutions that reveal the underlying structure of the equation and its solutions. Additionally, bifurcation analysis was conducted to understand the qualitative shifts in the system's behavior. We investigated sensitivity to initial conditions and the presence of unusual attractors to better comprehend the system's chaotic dynamics. While invariant solutions provide exact representations of certain dynamical states, bifurcation and chaos analyses offer insights into the system's intrinsic transitions and complexity. This study not only enhances the theoretical understanding of high-dimensional nonlinear evolution equations but also provides a foundation for future applications in various fields where complex processes are modeled by such equations.http://www.sciencedirect.com/science/article/pii/S2090447924005574(3+1)-dimensional evolution equationNon-classical symmetry analysisInvariant solutionsBifurcation analysisSensitivity analysis |
| spellingShingle | Ibtehal Alazman Manvendra Narayan Mishra Badr Saad T. Alkahtani Mati ur Rahman Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation Ain Shams Engineering Journal (3+1)-dimensional evolution equation Non-classical symmetry analysis Invariant solutions Bifurcation analysis Sensitivity analysis |
| title | Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation |
| title_full | Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation |
| title_fullStr | Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation |
| title_full_unstemmed | Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation |
| title_short | Exploring the non-classical symmetry, bifurcation with sensitivity analysis of a (3 + 1)-dimensional nonlinear evolution equation |
| title_sort | exploring the non classical symmetry bifurcation with sensitivity analysis of a 3 1 dimensional nonlinear evolution equation |
| topic | (3+1)-dimensional evolution equation Non-classical symmetry analysis Invariant solutions Bifurcation analysis Sensitivity analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2090447924005574 |
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