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<p>This study focuses on analyzing a system of nonlinear three-component dispersive interaction model, which is commonly used to model the propagation of complex wave structures in fiber optics. The main objective is to derive the exact analytical solutions and examine the dynamical behavior of the system. To achieve this, the novel extended hyperbolic function (EHF) method is employed due its effectiveness in constructing closed-form solutions for the nonlinear evolution equations. Using this method, various exact solutions are obtained including localized soliton, singular, periodic, rational, and algebraic wave solutions expressed in hyperbolic, trigonometric, rational, and exponential forms. In addition, the dynamical properties of the model are analyzed through the phase portraits, bifurcation behavior and sensitivity to initial conditions. Chaotic and quasi-periodic behaviors are further examined under external perturbations. Multistability analysis and Lyapunov exponent calculations confirm the coexistence of multiple stable states and reveal chaotic regions for specific parameter values. The obtained results extend the existing literature on nonlinear dispersive systems and provide deeper insight into complex wave propagation in fiber optics and related nonlinear physical systems.</p>

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Analytical and dynamical investigation of a three-component nonlinear dispersive interaction model

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Shah Muhammad,
  • Zainab Bibi,
  • Naseem Abbas,
  • Muhammad Idrees

摘要

This study focuses on analyzing a system of nonlinear three-component dispersive interaction model, which is commonly used to model the propagation of complex wave structures in fiber optics. The main objective is to derive the exact analytical solutions and examine the dynamical behavior of the system. To achieve this, the novel extended hyperbolic function (EHF) method is employed due its effectiveness in constructing closed-form solutions for the nonlinear evolution equations. Using this method, various exact solutions are obtained including localized soliton, singular, periodic, rational, and algebraic wave solutions expressed in hyperbolic, trigonometric, rational, and exponential forms. In addition, the dynamical properties of the model are analyzed through the phase portraits, bifurcation behavior and sensitivity to initial conditions. Chaotic and quasi-periodic behaviors are further examined under external perturbations. Multistability analysis and Lyapunov exponent calculations confirm the coexistence of multiple stable states and reveal chaotic regions for specific parameter values. The obtained results extend the existing literature on nonlinear dispersive systems and provide deeper insight into complex wave propagation in fiber optics and related nonlinear physical systems.