Research Article Extended Split-Step Fourier Transform Approach for Accurate Characterization of Soliton Propagation in a Lossy Optical Fiber Neveen G. A. Farag , 1 Ahmed H. Eltanboly, 1 M. S. El-Azab, 1 and S. S. A. Obayya 2,3 1 Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt 2 Centre for Photonics and Smart Materials, Zewail City of Science and Technology, October Gardens, 6th of October City, Giza 12578, Egypt 3 Electronics and Communications Engineering Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt Correspondence should be addressed to Neveen G. A. Farag; eng_neveen@hotmail.com Received 1 December 2021; Revised 31 January 2022; Accepted 17 February 2022; Published 8 March 2022 Academic Editor: Youssri Hassan Youssri Copyright © 2022 Neveen G. A. Farag et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we present a novel extension of the well-known split-step Fourier transform (SSFT) approach for solving the one- dimensional nonlinear Schrödinger equation (NLSE), which incorporates the fiber loss term. While this essential equation governs the pulse propagation in a lossy optical fiber, it is not supported by an exact analytical solution. In this regard, extended versions of the Fourier pseudospectral method (FPSM) and Hopscotch method (HSM) are effectively established as well to cope with the fiber losses effects associated with the pulses’ propagation through the fiber optics, and thus, numerous comparisons are exhaustively conducted among these three compelling numerical approaches to validate their reliability, stability, and accuracy. Based on this, the MATLAB numerical findings bolster that the extended version of the SSFT approach demonstrates superior performance over the other suggested schemes in simulating the solitons propagation in a lossy optical fiber. 1. Introduction A soliton, or what is also known as a solitary wave, is a self- reinforcing wave packet that sustains both its form and velocity while propagation, regardless of the travelling dis- tance or presence of obstacles. This shape conservation property makes it potentially compatible with the long- distance expansive data transmission [1]. Moreover, a cancellation of nonlinear and dispersive effects in the prop- agation medium, which is a basic feature that invariably occurs in the optical fibers, causes solitons. In other words, the term soliton refers to any optical pulse that resists chang- ing when it is transferred from the source to the destination due to a sensitive balance between the nonlinear and linear effects in the medium [2]. Therefore, the solitons are utterly beneficial in transporting information through optical fibers in a variety of modern communication systems because they demonstrate a robust grasp in achieving high bit rate trans- mission while minimizing error possibilities. This occurs due to their propagation without any distortion or shape chang- ing while moving through a lossless medium, which guaran- tees retaining the information stored in them until they reach the desired location [3]. This means that solitons pulses have incredibly stable characteristics in propagation through the transmission path due to its powerful resistance to the distortion effects, which resulted from the nonlinear- ity and dispersion and inherited in the optical fibers. However, the only serious damage that may change their shapes while propagation is the attenuation caused by the fiber losses. Thus, numerous researchers have suggested to compensate these fiber losses by the aid of the amplification in order to mitigate the functionality of the all-optical transmission system [4]. The optical fiber, where the solitons always propagate, is an extremely fine and thin pure glass that is usually made of pure silica. This fascinating fiber simulates the function of a waveguide in transmitting light pulses through the fiber ends because it comprises a transparent core surrounded by a lower refraction index transparent cladding material; this unique structure, presented in Figure 1 [5], confines the light Hindawi Journal of Function Spaces Volume 2022, Article ID 8316404, 17 pages https://doi.org/10.1155/2022/8316404