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<p>In this work, we study the nonlinear Schrödinger equation based on Kudryashov’s law of nonlinear refractive index, which arises from both the dual form of the quadrupled power law and nonlocal nonlinearity. By employing the auxiliary equation method, we obtain various optical solutions for the proposed problem conformable derivative. The new optical solutions are expressed through exponential and hyperbolic functions. These solutions include several types, such as bell-shaped, kink-type, wave, mixed dark-bright, and singular soliton solutions. Further, to emphasize the importance of these results, we depict the dynamics of various innovative exact solutions via graphical representations, considering different values of the conformable and temporal parameters. Additionally, the study highlights the significance of incorporating higher-order nonlinearity, offering a more comprehensive framework for understanding soliton dynamics and wave propagation in optical fibers. This investigation delves into the intriguing realm of wave propagation and soliton dynamics, offering a deeper comprehension of these phenomena and advancing the study of optical fiber systems.</p>

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The formulation of soliton solutions for Kudryashov’s law with a dual form of generalized non-local nonlinearity and Kudryashov’s refractive index in optical fiber

  • 期刊论文

  • 发表日期：

    2025年2月21日

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  • Mohammed Sadeq Salih,
  • Muhammad Amin S. Murad

摘要

In this work, we study the nonlinear Schrödinger equation based on Kudryashov’s law of nonlinear refractive index, which arises from both the dual form of the quadrupled power law and nonlocal nonlinearity. By employing the auxiliary equation method, we obtain various optical solutions for the proposed problem conformable derivative. The new optical solutions are expressed through exponential and hyperbolic functions. These solutions include several types, such as bell-shaped, kink-type, wave, mixed dark-bright, and singular soliton solutions. Further, to emphasize the importance of these results, we depict the dynamics of various innovative exact solutions via graphical representations, considering different values of the conformable and temporal parameters. Additionally, the study highlights the significance of incorporating higher-order nonlinearity, offering a more comprehensive framework for understanding soliton dynamics and wave propagation in optical fibers. This investigation delves into the intriguing realm of wave propagation and soliton dynamics, offering a deeper comprehension of these phenomena and advancing the study of optical fiber systems.