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<p>This exposition articulates an examination of the <i>q</i>-deformed Tanh-Gordon equation to derive novel optical solitons, which have significant implications in quantum mechanics and optical physics. The extended hyperbolic function approach generates a spectrum of soliton solutions, including peakon, bright, singular, periodic, single-hump, and periodic singular structures, within a well-defined parameter space. These solutions serve as essential illustrations of the intricate structure and diverse dynamics present in nonlinear higher-dimensional systems. Their graphical representation through 3D, 2D, and contour plots enhances understanding. Furthermore, a rigorous dynamical analysis investigates bifurcation structures and chaotic behavior using instruments such as time series, phase diagrams, Poincaré maps, Lyapunov exponents, and the power spectrum. The considered system is also investigated for multistability using different initial conditions, showing that small perturbations in initial conditions can induce transitions between stable and unstable states. The outcomes are further validated through phase portraits, reinforcing the reliability of the solutions. The obtained results are useful to understand the behavior of nonlinear wave phenomena and their real-world utilization.</p>

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Soliton Solutions and Qualitative Insights: A Comprehensive Study of the q-Deformed Tanh-Gordon Equation

  • 期刊论文

  • 发表日期：

    2025年5月31日

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  • Asma Rashid Butt,
  • Zainab Rana,
  • Younes Chahlaoui,
  • Ahmet Bekir

摘要

This exposition articulates an examination of the q-deformed Tanh-Gordon equation to derive novel optical solitons, which have significant implications in quantum mechanics and optical physics. The extended hyperbolic function approach generates a spectrum of soliton solutions, including peakon, bright, singular, periodic, single-hump, and periodic singular structures, within a well-defined parameter space. These solutions serve as essential illustrations of the intricate structure and diverse dynamics present in nonlinear higher-dimensional systems. Their graphical representation through 3D, 2D, and contour plots enhances understanding. Furthermore, a rigorous dynamical analysis investigates bifurcation structures and chaotic behavior using instruments such as time series, phase diagrams, Poincaré maps, Lyapunov exponents, and the power spectrum. The considered system is also investigated for multistability using different initial conditions, showing that small perturbations in initial conditions can induce transitions between stable and unstable states. The outcomes are further validated through phase portraits, reinforcing the reliability of the solutions. The obtained results are useful to understand the behavior of nonlinear wave phenomena and their real-world utilization.