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<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6074_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(\cos \omega t\)</EquationSource> </InlineEquation> is added. Numerical simulations demonstrate how changes in frequency and amplitude impact the dynamics of the system.</p>

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Bifurcation Analysis and Soliton Structures of Davey-Stewartson Fokas System

  • 期刊论文

  • 发表日期：

    2025年7月17日

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  • Muhammad Hammad,
  • Amjad Hussain

摘要

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 \(\cos \omega t\) is added. Numerical simulations demonstrate how changes in frequency and amplitude impact the dynamics of the system.