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<p>The Jacobi elliptic function (JEF) method and other advanced tools are used in this study to explore solitary wave solutions and the dynamical behavior of the (2+1)-dimensional Resonant Davey–Stewartson (RDS) equations. Although prior studies have concentrated on the soliton solutions of RDS equations, there is a deficiency in the literature concerning the application of the JEF approach. However, we found no research work that highlights the quasi-periodic and chaotic behavior of the RDS system. We obtain analytical solutions for the RDS model by turning it into a nonlinear ordinary differential equation. The resulting equation is solved using the JEF approach. We visualize these solutions through three-dimensional graphs, revealing their structural properties. These graphs include dark and bright solitary wave profiles. To study how the system changes over time, we use contour and surface plots to display the energy landscape, along with energy function plots that illustrate energy levels and the system’s behavior at different energy states. We also use phase portraits, Lyapunov exponents, and sensitivity studies to explore the system’s behaviors in greater detail.</p>

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Jacobi elliptic function solutions and bifurcation analysis of (2+1)-dimensional resonant Davey–Stewartson equations

  • 期刊论文

  • 发表日期：

    2026年1月30日

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  • Muhammad Zeeshan,
  • Amjad Hussain,
  • Adil Jhangeer,
  • Muhammad Junaid-U-Rehman

摘要

The Jacobi elliptic function (JEF) method and other advanced tools are used in this study to explore solitary wave solutions and the dynamical behavior of the (2+1)-dimensional Resonant Davey–Stewartson (RDS) equations. Although prior studies have concentrated on the soliton solutions of RDS equations, there is a deficiency in the literature concerning the application of the JEF approach. However, we found no research work that highlights the quasi-periodic and chaotic behavior of the RDS system. We obtain analytical solutions for the RDS model by turning it into a nonlinear ordinary differential equation. The resulting equation is solved using the JEF approach. We visualize these solutions through three-dimensional graphs, revealing their structural properties. These graphs include dark and bright solitary wave profiles. To study how the system changes over time, we use contour and surface plots to display the energy landscape, along with energy function plots that illustrate energy levels and the system’s behavior at different energy states. We also use phase portraits, Lyapunov exponents, and sensitivity studies to explore the system’s behaviors in greater detail.