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Bifurcation Analysis and Soliton Structures of Davey-Stewartson Fokas System.

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Title: Bifurcation Analysis and Soliton Structures of Davey-Stewartson Fokas System.
Authors: Hammad, Muhammad1 (AUTHOR) hammad.22311039@math.qau.edu.pk, Hussain, Amjad1 (AUTHOR) a.hussain@qau.edu.pk
Source: International Journal of Theoretical Physics. Aug2025, Vol. 64 Issue 8, p1-23. 23p.
Subjects: Dynamical systems, Poincare maps (Mathematics), Computational mathematics, Applied mathematics, Mathematical physics
Abstract: In this research, we studied the (2+1)-dimensional Davey-Stewartson Fokas (DS-Fokas) system, which serves as an optimal model for nonlinear pulse propagation in mono-mode optical fibers. We employ the Jacobi elliptic function approach to obtain the novel soliton solutions for the DS-Fokas system. The employed method is a very efficient and robust mathematical approach for solving non-linear models of various nonlinear Schrödinger's equations (NLSEs) in mathematical physics and sciences. The obtained solutions are useful and significant in elucidating the DS-Fokas system's physical aspects, as they provide insights. Furthermore, we discuss these obtained solutions graphically using 3D and 2D graphs to gain a deep understanding and vision of the analytical results. We also looked at the unpredictable and changing behaviors of the system we studied by using phase portraits, quasi-periodic and chaotic portraits, Poincare maps, bifurcation diagrams, and sensitivity. The theory of planar dynamical systems looks at chaotic patterns in the systems under study when the disturbance term is added. Numerical simulations demonstrate how changes in frequency and amplitude impact the dynamics of the system. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Theoretical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Theoretical+Physics%22">International Journal of Theoretical Physics</searchLink>. Aug2025, Vol. 64 Issue 8, p1-23. 23p.
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  Data: <searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Poincare+maps+%28Mathematics%29%22">Poincare maps (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+mathematics%22">Computational mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Applied+mathematics%22">Applied mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+physics%22">Mathematical physics</searchLink>
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  Data: In this research, we studied the (2+1)-dimensional Davey-Stewartson Fokas (DS-Fokas) system, which serves as an optimal model for nonlinear pulse propagation in mono-mode optical fibers. We employ the Jacobi elliptic function approach to obtain the novel soliton solutions for the DS-Fokas system. The employed method is a very efficient and robust mathematical approach for solving non-linear models of various nonlinear Schrödinger's equations (NLSEs) in mathematical physics and sciences. The obtained solutions are useful and significant in elucidating the DS-Fokas system's physical aspects, as they provide insights. Furthermore, we discuss these obtained solutions graphically using 3D and 2D graphs to gain a deep understanding and vision of the analytical results. We also looked at the unpredictable and changing behaviors of the system we studied by using phase portraits, quasi-periodic and chaotic portraits, Poincare maps, bifurcation diagrams, and sensitivity. The theory of planar dynamical systems looks at chaotic patterns in the systems under study when the disturbance term is added. Numerical simulations demonstrate how changes in frequency and amplitude impact the dynamics of the system. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of International Journal of Theoretical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: Aug2025
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