Hussain Akhtar, Ibrahim Tarek F, Alanazi Faizah D, Osman Waleed M, Dawood Arafa A, Herrera Jorge
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
Department of Mathematics, College Sciences at Mahail Aseer, King Khalid University, Abha, Saudi Arabia.
Sci Rep. 2025 Sep 1;15(1):32069. doi: 10.1038/s41598-025-05064-3.
The nonlinear Chen-Lee-Liu (NCLL) model is a crucial mathematical model for assessing optical fiber communication systems. It incorporates various factors, including noise, dispersion, and nonlinearity, which can influence signal quality and data transmission rates within optical fiber networks. The NCLL model can be employed to optimize the design of optical fiber systems. In this study, we investigated solitary and soliton solutions applicable to the optics of the NCLL model with a beta derivative by utilizing a new extended hyperbolic function (NEHF) and generalized exponential rational function (NGERF) methods. Using symbolic computations, the NEHF method generates closed-form solutions to the NCLL equation, which is expressed in hyperbolic, trigonometric, polynomial, and exponential form. By contrast, the NGERF method generates closed-form solutions described in hyperbolic, trigonometric, and exponential forms, offering various solution types. The model exhibits various soliton solutions, including periodic oscillating nonlinear waves, kink-wave profiles, multiple soliton profiles, singular solutions, mixed singular solutions, mixed hyperbolic solutions, periodic patterns with anti-troughs and anti-peaked crests, mixed periodic solutions, mixed complex solitary shock solutions, mixed shock singular solutions, mixed trigonometric solutions, and periodic solutions. Using symbolic computation tools, such as Mathematica 11.3 or Maple, these newly derived soliton solutions were verified by substituting them back into the corresponding system. The findings of this study demonstrate that the applied methodologies are reliable, efficient, and capable of generating optical soliton solutions for more complex wave equations in optical fiber communication systems.
非线性陈-李-刘（NCLL）模型是评估光纤通信系统的关键数学模型。它纳入了各种因素，包括噪声、色散和非线性，这些因素会影响光纤网络内的信号质量和数据传输速率。NCLL模型可用于优化光纤系统的设计。在本研究中，我们通过利用一种新的扩展双曲函数（NEHF）和广义指数有理函数（NGERF）方法，研究了适用于具有β导数的NCLL模型光学的孤立子和孤子解。使用符号计算，NEHF方法生成了NCLL方程的封闭形式解，该解以双曲、三角、多项式和指数形式表示。相比之下，NGERF方法生成了以双曲、三角和指数形式描述的封闭形式解，提供了各种解类型。该模型展示了各种孤子解，包括周期性振荡非线性波、扭结波剖面、多个孤子剖面、奇异解、混合奇异解、混合双曲解、具有反波谷和反尖峰的周期性模式、混合周期解、混合复孤立激波解、混合激波奇异解、混合三角解和周期解。使用诸如Mathematica 11.3或Maple等符号计算工具，通过将这些新推导的孤子解代入相应系统进行了验证。本研究结果表明，所应用的方法可靠、高效，能够为光纤通信系统中更复杂的波动方程生成光学孤子解。
