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<p>This study employs symbolic computational techniques to examine a third-order nonlinear Schrödinger equation as an extended model for soliton transmission in optical wave orientation. The extended trial equation method generates exact traveling wave solutions, including singular, soliton, rational function, and elliptic integral function solutions. In contrast, the generalized Arnous method constructs solutions such as dark-singular solitons, pure cubic dark solitons, and singular combinations, providing a diverse spectrum of solutions. The qualitative behavior of the resulting dynamical system is analyzed through bifurcation and chaotic analyses, revealing its sensitivity to initial condition variations. Graphical representations, including soliton profiles and phase portraits, illustrate the findings. All newly generated soliton solutions have not been published in the literature. These solutions are verified by substituting them back into the associated system using Maple Software. This study offers important insights into long-term behavior and helps design stable and robust systems across various fields, such as optical fibers, data transmission, nonlinear optics, and long-distance communication. These methods enhance understanding of nonlinear dynamical models, significantly contributing to studying complex systems in various scientific and engineering domains.</p>

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Nonlinear Shrödinger equation having self-phase modulation without chromatic dispersion: sensitivity analysis and novel soliton solutions

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Anjli Khatkar,
  • Fathima Shehla,
  • Alka Sharma,
  • Sachin Kumar,
  • Ravindra Yadav,
  • Sandeep Malik

摘要

This study employs symbolic computational techniques to examine a third-order nonlinear Schrödinger equation as an extended model for soliton transmission in optical wave orientation. The extended trial equation method generates exact traveling wave solutions, including singular, soliton, rational function, and elliptic integral function solutions. In contrast, the generalized Arnous method constructs solutions such as dark-singular solitons, pure cubic dark solitons, and singular combinations, providing a diverse spectrum of solutions. The qualitative behavior of the resulting dynamical system is analyzed through bifurcation and chaotic analyses, revealing its sensitivity to initial condition variations. Graphical representations, including soliton profiles and phase portraits, illustrate the findings. All newly generated soliton solutions have not been published in the literature. These solutions are verified by substituting them back into the associated system using Maple Software. This study offers important insights into long-term behavior and helps design stable and robust systems across various fields, such as optical fibers, data transmission, nonlinear optics, and long-distance communication. These methods enhance understanding of nonlinear dynamical models, significantly contributing to studying complex systems in various scientific and engineering domains.