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<p>This study develops exact soliton solutions for the (2+1)-dimensional Kundu–Mukherjee– Naskar equation, a versatile model describing signal transmission in telecommunications and long-distance optical fiber pulse propagation. The equation is reduced to a nonlinear ordinary differential form using a traveling wave transformation derived from Lie symmetry infinitesimals. Two analytical approaches, the modified Sardar sub-equation method and the modified auxiliary equation method, are applied to obtain diverse classes of solutions, including hyperbolic, Jacobi, trigonometric, and rational forms. Numerical simulations, performed in <Emphasis FontCategory="NonProportional">MATLAB</Emphasis>, visualize bright, dark, singular, kink, periodic, and anti-kink soliton structures through 3D, 2D, and density plots. The sensitivity of the dynamical system to changes in initial conditions is analyzed, with Lyapunov exponents computed to quantify its stability and dynamic complexity. Both qualitative and quantitative perspectives are considered. The results are significant for optical fiber communications, where such stable soliton solutions can minimize signal distortion, enhance transmission quality, and support high-capacity, long-distance data transfer.</p>

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Exploring optical soliton solution for (2+ 1)-dimensional Kundu–Mukherjee–Naskar equation using two analytical methods with sensitivity analysis

  • 期刊论文

  • 发表日期：

    2025年10月14日

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  • Muhammad Imran Asjad,
  • Azad Ali Sagher,
  • Muhammad Bilal Riaz,
  • Suhad Ali Osman Abdallah

摘要

This study develops exact soliton solutions for the (2+1)-dimensional Kundu–Mukherjee– Naskar equation, a versatile model describing signal transmission in telecommunications and long-distance optical fiber pulse propagation. The equation is reduced to a nonlinear ordinary differential form using a traveling wave transformation derived from Lie symmetry infinitesimals. Two analytical approaches, the modified Sardar sub-equation method and the modified auxiliary equation method, are applied to obtain diverse classes of solutions, including hyperbolic, Jacobi, trigonometric, and rational forms. Numerical simulations, performed in MATLAB, visualize bright, dark, singular, kink, periodic, and anti-kink soliton structures through 3D, 2D, and density plots. The sensitivity of the dynamical system to changes in initial conditions is analyzed, with Lyapunov exponents computed to quantify its stability and dynamic complexity. Both qualitative and quantitative perspectives are considered. The results are significant for optical fiber communications, where such stable soliton solutions can minimize signal distortion, enhance transmission quality, and support high-capacity, long-distance data transfer.