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<p>In this study, we investigate the cubic-quartic resonant nonlinear Schrödinger equation (CQRNSE) under a parabolic law to obtain various categories of optical solutions, including bright, dark, singular soliton, rational wave and singular periodic wave solutions. The CQRNSE describes wave propagation in fiber optics. The modified F-expansion method is a powerful technique employed to construct these solutions. Additionally, using bifurcation theory, we derive the associated Hamiltonian function and analyze the corresponding phase portraits. To graphically illustrate and exhibit the obtained solutions, we present them in both 3D and 2D formats. Furthermore, Poincaré sections and bifurcation diagram are used to analyze periodic, quasi-periodic, and chaotic behaviors of the related dynamic system, along with the system’s sensitivity to initial conditions. The findings of this research are fascinating and make a significant contribution to the domain of solitons in particular, and to the broader field of mathematical physics. The approach used in this work yields a variety of new solitary and soliton wave solutions, which will be valuable for researchers applying these models to real-world problems.</p>

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Dynamical system, chaotic behavior, and sensitivity of the resonant nonlinear Schrödinger equation with the parabolic law

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Ibrahim S. Hamad,
  • Karmina K. Ali

摘要

In this study, we investigate the cubic-quartic resonant nonlinear Schrödinger equation (CQRNSE) under a parabolic law to obtain various categories of optical solutions, including bright, dark, singular soliton, rational wave and singular periodic wave solutions. The CQRNSE describes wave propagation in fiber optics. The modified F-expansion method is a powerful technique employed to construct these solutions. Additionally, using bifurcation theory, we derive the associated Hamiltonian function and analyze the corresponding phase portraits. To graphically illustrate and exhibit the obtained solutions, we present them in both 3D and 2D formats. Furthermore, Poincaré sections and bifurcation diagram are used to analyze periodic, quasi-periodic, and chaotic behaviors of the related dynamic system, along with the system’s sensitivity to initial conditions. The findings of this research are fascinating and make a significant contribution to the domain of solitons in particular, and to the broader field of mathematical physics. The approach used in this work yields a variety of new solitary and soliton wave solutions, which will be valuable for researchers applying these models to real-world problems.