Jurnal Fisika Unand (JFU) Vol. 11, No. 3, Juli 2022, hal.387 – 392 ISSN: 2302-8491 (Print); 2686-2433 (Online) https://doi.org/10.25077/jfu.11.3.387-392.2022 Creative Commons Attribution 4.0 License http://jfu.fmipa.unand.ac.id/ 387 Open Access The Bilinear Formula in Soliton Theory of Optical Fibers Nando Saputra*, Ahmad Ripai, Zulfi Abdullah Theoretical Physics Laboratory, Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Kampus Unand Limau Manis, Padang 25163, Indonesia. Article Info ABSTRACT Article History: Received: 5 April 2022 Revised: 5 July 2022 Accepted: 5 July 2022 Solitons are wave phenomena or pulses that can maintain their shape stability when propagating in a medium. In optical fibers, they become general solutions of the Non-Linear Schrödinger Equation (NLSE). Despite its mathematical complexity, NLSE has been an interesting issue. Soliton analysis and mathematical techniques to solve problems of the equation keep doing. In this paper, we review the form of the bilinear formula for the case. We re-observed a one-soliton solution, their stability, and like soliton trains based on the formula, also verified the work of the last researcher. Here, the mathematical parameters of position α (0) and phase η are verified to become features of change in horizontal position and phase of one soliton in the (z, t) plane during propagation. In addition, we notice the soliton has established stability. Finally, for the condition Kerr effect focusing or the group velocity dispersion β2 more dominates, we present like the soliton trains in optical fibers under modulation instability of plane wave. Copyright © 2022 Author(s). All rights reserved Keywords: bilinear formula modulation instability NLSE one-soliton optical fiber Corresponding Author: Nando Saputra Email: nandosaputra08@gmail.com I. INTRODUCTION Technology has become a device and a primary human need in the modern world of communication. Reducing loss and improving the transmission quality of the technological communication system is the greatest challenge. The utilization of optical fibers is one of the alternative questions to answer. However, in modern optical fiber communication, loss, transmission quality, and information capacity issues have increasingly become a concern (Yan, X. W. & Chen, 2022). Hence, we need an idea that supports the optimal and efficient control of the information transmission process. It is the offering to process the transmission of information in the form of soliton pulses (Liu, W. J., Tian, B., Zhang, H. Q., Li, L. L. & Xue, 2008). Hasegawa, A. & Tappert (1973) was the first scientist to present soliton pulses to reduce loss issues in optical fiber transmission of information. It is a theoretical concept regarding modeling an optical beam (information carrier) into a single wave packet (soliton pulses) stable in fibers during propagation. The solitons theory in optical fiber has attracted considerable attention (Chen, X., Sun, Y., Gao, Y., Yan, X., Zhang, X., Wang, F., Suzuki, T., Ohishi, Y. & Cheng, 2021; Ripai, A., Abdullah, Z., Syafwan, M. & Hidayat, 2020; Yan, X. W. & Chen, 2022). Theoretically, we know fiber solitons dynamics obtainable formulated by the Non-Linear Schrödinger Equation (NLSE) (Agrawal, 2013). Its stability is clear from the right balance between the nonlinearity and the dispersion properties of optical fibers (Agrawal, 2013; Ripai, A., Abdullah, Z., Syafwan, M. & Hidayat, 2020). Only second-order dispersion is familiar considered in the equation yet. It urges our understanding of the bright soliton existence in the anomalous dispersion regime and dark solitons (the intensity profile contains a dip in a uniform background) in a normal dispersion regime (Mei-Hua, L., You-Shen, X. & Ji, 2004). When short pulses are considered (to nearly 50 fs), third-order dispersion becomes essential, so it must include in the NLSE model. Then, as the pulse width becomes even narrower (below 10 fs), the fourth-order dispersion must also be considered (Palacios, S. L. & Fernández-Diaz, 2001).