Scholarlink

<p>This study investigates the analytical and dynamical behavior of the modified Benjamin–Bona–Mahony equation, a fundamental model in fluid dynamics describing uni-directional water waves with small amplitudes influenced by dispersion and nonlinear effects. The research applies the generalized Arnous method to derive analytical solutions, which are visualized through 3D, 2D, and contour plots using Mathematica software. To analyze the equation’s qualitative dynamics, bifurcation, and chaotic behavior are examined by identifying critical bifurcation points and chaotic patterns induced by external forces. Chaotic behavior is detected using a chaotic attractor, fractal dimension, power spectrum, and return map in MATLAB software. The stability, sensitivity, and multistability of the system under varying initial conditions are assessed through numerical simulations in MATLAB software. Compared to existing works, the proposed approach provides a more comprehensive characterization of the equation’s nonlinear behavior, capturing intricate dynamical transitions with improved accuracy. These findings contribute to advancing nonlinear wave theory with potential applications in nonlinear fiber optics and telecommunications.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Analytical solutions and dynamical insights of the modified Benjamin–Bona–Mahony equation with applications in nonlinear optics

  • 期刊论文

  • 发表日期：

    2025年4月30日

查看全文
  • Beenish,
  • Maria Samreen

摘要

This study investigates the analytical and dynamical behavior of the modified Benjamin–Bona–Mahony equation, a fundamental model in fluid dynamics describing uni-directional water waves with small amplitudes influenced by dispersion and nonlinear effects. The research applies the generalized Arnous method to derive analytical solutions, which are visualized through 3D, 2D, and contour plots using Mathematica software. To analyze the equation’s qualitative dynamics, bifurcation, and chaotic behavior are examined by identifying critical bifurcation points and chaotic patterns induced by external forces. Chaotic behavior is detected using a chaotic attractor, fractal dimension, power spectrum, and return map in MATLAB software. The stability, sensitivity, and multistability of the system under varying initial conditions are assessed through numerical simulations in MATLAB software. Compared to existing works, the proposed approach provides a more comprehensive characterization of the equation’s nonlinear behavior, capturing intricate dynamical transitions with improved accuracy. These findings contribute to advancing nonlinear wave theory with potential applications in nonlinear fiber optics and telecommunications.