Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system
In various fields of nonlinear sciences, fractional derivatives improve the accuracy and understanding of nonlinear dynamics. This study explores the fractional (2+1) dimensional nonlinear Schrödinger equation arising in the diversity of engineering fields. A variety of solitary wave solutions have...
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| Format: | Article |
| 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/S2090447924006233 |
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| author | Usman Younas Ejaz Hussain Jan Muhammad Mubariz Garayev Mohammed El-Meligy |
| author_facet | Usman Younas Ejaz Hussain Jan Muhammad Mubariz Garayev Mohammed El-Meligy |
| author_sort | Usman Younas |
| collection | DOAJ |
| description | In various fields of nonlinear sciences, fractional derivatives improve the accuracy and understanding of nonlinear dynamics. This study explores the fractional (2+1) dimensional nonlinear Schrödinger equation arising in the diversity of engineering fields. A variety of solitary wave solutions have been discussed with the assistance of advanced integration methods, namely the modified generalized Riccati equation mapping approach and F-expansion technique. The obtained solutions are displayed in graphs of relevant parameter values to elucidate the physical meaning and scientific interpretation of the analytical work. This paper's main contribution is an examination of the qualitative study like sensitivity analysis, chaotic behavior, and bifurcation analysis. The Galilean transformation is used for the qualitative analysis. Additionally, the behavior of time-varying dynamical systems is investigated through the perspective of chaos theory. To uncover the evasive character of chaos, we investigate 3D, 2D, phase portraits, time series, and Poincare mapping as potent instruments. |
| format | Article |
| id | doaj-art-a5928c663918440b8da5e1eefc0e2f94 |
| 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-a5928c663918440b8da5e1eefc0e2f942025-01-17T04:49:27ZengElsevierAin Shams Engineering Journal2090-44792025-01-01161103242Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical systemUsman Younas0Ejaz Hussain1Jan Muhammad2Mubariz Garayev3Mohammed El-Meligy4Department of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, ChinaDepartment of Mathematics, University of the Punjab, Pakistan; Corresponding author.Department of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, ChinaDepartment of Mathematics, College of Science, King Saud University, Riyadh, Saudi ArabiaJadara University Research Center, Jadara University, Jordan; Applied Science Research Center, Applied Science Private University, Amman, JordanIn various fields of nonlinear sciences, fractional derivatives improve the accuracy and understanding of nonlinear dynamics. This study explores the fractional (2+1) dimensional nonlinear Schrödinger equation arising in the diversity of engineering fields. A variety of solitary wave solutions have been discussed with the assistance of advanced integration methods, namely the modified generalized Riccati equation mapping approach and F-expansion technique. The obtained solutions are displayed in graphs of relevant parameter values to elucidate the physical meaning and scientific interpretation of the analytical work. This paper's main contribution is an examination of the qualitative study like sensitivity analysis, chaotic behavior, and bifurcation analysis. The Galilean transformation is used for the qualitative analysis. Additionally, the behavior of time-varying dynamical systems is investigated through the perspective of chaos theory. To uncover the evasive character of chaos, we investigate 3D, 2D, phase portraits, time series, and Poincare mapping as potent instruments.http://www.sciencedirect.com/science/article/pii/S2090447924006233Optical solitonsM-fractional derivativeF-expansion techniqueGeneralized modified Riccati equation mapping approachQualitative analysis |
| spellingShingle | Usman Younas Ejaz Hussain Jan Muhammad Mubariz Garayev Mohammed El-Meligy Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system Ain Shams Engineering Journal Optical solitons M-fractional derivative F-expansion technique Generalized modified Riccati equation mapping approach Qualitative analysis |
| title | Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system |
| title_full | Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system |
| title_fullStr | Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system |
| title_full_unstemmed | Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system |
| title_short | Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system |
| title_sort | bifurcation analysis chaotic behavior sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system |
| topic | Optical solitons M-fractional derivative F-expansion technique Generalized modified Riccati equation mapping approach Qualitative analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2090447924006233 |
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