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<p>Bifurcation, chaos, and soliton are critical phenomena in nonlinear dynamical systems, enhancing our understanding of complex physical processes. In this work, we explore these phenomena through the theory of the Manakov equation, a widely studied framework in optics, plasma physics, and Bose–Einstein condensates. We obtain the soliton solution for the nonlinear problem using the unified solver process, and we derive the dynamical system from the Galilean transformation. Using planar dynamics, we investigate bifurcations, chaos, and sensitivity within the system. This study reveals quasi-periodic, periodic, and chaotic behaviors and visualizes various soliton constructions, including bright, dark, kink, and anti-kink waves. We utilize 3D and 2D phase diagrams, Lyapunov exponents, Poincaré maps, bifurcation diagrams, fractal dimensions, strange attractors, recurrence plots, and return maps to detect and analyze chaos. Therefore, this study advances our understanding of waveform shape, chaos, and bifurcation analysis, offering novel insights into wave dynamics and design.</p>

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Bifurcation, chaos, and soliton analysis of the Manakov equation

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Abdul Hamid Ganie,
  • Md. Shahidur Rahaman,
  • Feryal Abdullah Aladsani,
  • Mohammad Safi Ullah

摘要

Bifurcation, chaos, and soliton are critical phenomena in nonlinear dynamical systems, enhancing our understanding of complex physical processes. In this work, we explore these phenomena through the theory of the Manakov equation, a widely studied framework in optics, plasma physics, and Bose–Einstein condensates. We obtain the soliton solution for the nonlinear problem using the unified solver process, and we derive the dynamical system from the Galilean transformation. Using planar dynamics, we investigate bifurcations, chaos, and sensitivity within the system. This study reveals quasi-periodic, periodic, and chaotic behaviors and visualizes various soliton constructions, including bright, dark, kink, and anti-kink waves. We utilize 3D and 2D phase diagrams, Lyapunov exponents, Poincaré maps, bifurcation diagrams, fractal dimensions, strange attractors, recurrence plots, and return maps to detect and analyze chaos. Therefore, this study advances our understanding of waveform shape, chaos, and bifurcation analysis, offering novel insights into wave dynamics and design.