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<p>In this article, we present a detailed investigation of the fractional coupled Higgs system, which is a prominent mathematical model in the field of relativistic quantum theory. By establishing the complex structure of this dynamical model, the study offers a robust framework for comprehending the propagation of long nonlinear waves. An advanced analytical technique, namely, the modified Sardar sub-equation method, is utilized to secure a diverse range of exact solutions to the proposed model. In addition, the dynamical features of the system are analyzed through different tools, including bifurcation, chaos, and sensitivity analysis, presenting valuable insights into the intricate behavior of the proposed model. The derived soliton solutions depict rich profiles, such as dark, dark-bright, W-shaped, singular, periodic, exponential, and mixed trigonometric forms. The physical relevance of these solutions is provided in the form of three-dimensional, two-dimensional, contour, and density graphs. The findings explore that the selected method is highly effective in exploring exact soliton solutions from complex nonlinear systems. This work demonstrates a strong foundation for future investigation in nonlinear sciences and expands its potential applications across various areas of applied mathematics and quantum physics.</p>

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Dynamics of bifurcation, chaos, sensitivity, and innovative soliton solutions with propagation insights into a fractional coupled Higgs system

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • Ibtehal Alazman

摘要

In this article, we present a detailed investigation of the fractional coupled Higgs system, which is a prominent mathematical model in the field of relativistic quantum theory. By establishing the complex structure of this dynamical model, the study offers a robust framework for comprehending the propagation of long nonlinear waves. An advanced analytical technique, namely, the modified Sardar sub-equation method, is utilized to secure a diverse range of exact solutions to the proposed model. In addition, the dynamical features of the system are analyzed through different tools, including bifurcation, chaos, and sensitivity analysis, presenting valuable insights into the intricate behavior of the proposed model. The derived soliton solutions depict rich profiles, such as dark, dark-bright, W-shaped, singular, periodic, exponential, and mixed trigonometric forms. The physical relevance of these solutions is provided in the form of three-dimensional, two-dimensional, contour, and density graphs. The findings explore that the selected method is highly effective in exploring exact soliton solutions from complex nonlinear systems. This work demonstrates a strong foundation for future investigation in nonlinear sciences and expands its potential applications across various areas of applied mathematics and quantum physics.