Journal of Applied Science and Engineering

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O. Gonzalez-Gaxiola1, Anjan Biswas2,3,4,5This email address is being protected from spambots. You need JavaScript enabled to view it., Yakup Yıldırım6,7, and Asim Asiri3

1Applied Mathematics and Systems Department, Universidad Autonoma Metropolitana–Cuajimalpa, Vasco de Quiroga 4871, 05348 Mexico City, Mexico

2Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245–2715, USA

3Mathematical Modeling and Applied Computation (MMAC) Research Group, Center of Modern Mathematical Sciences and their Applications (CMMSA), Department of Mathematics, King Abdulaziz University, Jeddah—21589, Saudi Arabia

4Department of Applied Sciences, Cross—Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati—800201, Romania

5Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa—0204, Pretoria, South Africa

6Department of Computer Engineering, Biruni University, Istanbul 34010, Turkey

7Department of Mathematics, Near East University, 99138 Nicosia, Cyprus



Received: July 5, 2023
Accepted: October 26, 2023
Publication Date: December 26, 2023

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

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This paper retrieves pure-cubic optical solitons for the nonlinear Schrödinger’s equation when chromatic dispersion term is dropped due to its low count. This model with the inclusion of third-order dispersion after dropping chromatic dispersion maintains the necessary balance between dispersion and self-phase modulation for the solitons to sustain. The Laplace-Adomian decomposition scheme is applied to recover such pure-cubic soliton solutions. The surface plots as well as the contour plots for bright and dark soliton solutions are displayed. The results are profoundly significant and novel. The numerical simulation for pure-cubic solitons is being reported for the very first time in this paper. While in the past, solitons were studied with chromatic dispersion, this is the first-time solitons are being addressed, and that too numerically, with pure-cubic dispersion format. The radiation effects are ignored to focus on the core soliton regime. The results are impressive and promising. The two-dimensional numerical simulation and the exact solutions to the model are almost a perfect match. The error table displays a measure of the order of 10−7.

Keywords: Pure-cubic optical solitons; Generalized third order NLSE; Cubic nonlinearity; Laplace-Adomian decomposition method

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