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<p>The Boiti–Leon–Pempinelli (BLP) system models nonlinear wave phenomena relevant to Bose–Einstein condensates, fluid dynamics, communication networks, and nonlinear optics. This work investigates soliton dynamics in nonlinear optical media by introducing a novel auxiliary equation method that yields new exact solutions, including kink, singular, exponential, rational, and U-shaped solitons. The physical characteristics of these solutions are illustrated through two- and three-dimensional and contour visualizations. A qualitative bifurcation analysis of the unperturbed system is performed using phase portraits. The introduction of an external forcing term reveals complex dynamical behaviors, including quasi-periodicity, chaos, and multi-stability. These behaviors are characterized using Lyapunov exponents, time series, phase space projections, and Poincaré sections. Numerical simulations based on the Runge–Kutta method confirm sensitivity to initial conditions. The results uncover previously unexplored dynamical features of the BLP system and demonstrate the effectiveness of the proposed analytical and numerical framework for nonlinear models in mathematical physics and engineering.</p>

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Novel soliton structures, bifurcation dynamics, and chaos analysis in the Boiti–Leon–Pempinelli system

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Ahmed M. Zian,
  • Zainab Bibi,
  • Naseem Abbas,
  • Akhtar Hussain

摘要

The Boiti–Leon–Pempinelli (BLP) system models nonlinear wave phenomena relevant to Bose–Einstein condensates, fluid dynamics, communication networks, and nonlinear optics. This work investigates soliton dynamics in nonlinear optical media by introducing a novel auxiliary equation method that yields new exact solutions, including kink, singular, exponential, rational, and U-shaped solitons. The physical characteristics of these solutions are illustrated through two- and three-dimensional and contour visualizations. A qualitative bifurcation analysis of the unperturbed system is performed using phase portraits. The introduction of an external forcing term reveals complex dynamical behaviors, including quasi-periodicity, chaos, and multi-stability. These behaviors are characterized using Lyapunov exponents, time series, phase space projections, and Poincaré sections. Numerical simulations based on the Runge–Kutta method confirm sensitivity to initial conditions. The results uncover previously unexplored dynamical features of the BLP system and demonstrate the effectiveness of the proposed analytical and numerical framework for nonlinear models in mathematical physics and engineering.