Open Access

ARTICLE

Optical Solitons with Parabolic and Weakly Nonlocal Law of Self-Phase Modulation by Laplace–Adomian Decomposition Method

Oswaldo González-Gaxiola¹, Anjan Biswas^2,3,4,*, Ahmed H. Arnous⁵, Yakup Yildirim^6,7

1 Applied Mathematics and Systems Department, Universidad Autónoma Metropolitana-Cuajimalpa, Vasco de Quiroga 4871, Mexico City, 05348, Mexico
2 Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245-2715, USA
3 Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, Galati, 800201, Romania
4 Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria, 0204, South Africa
5 Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El–Shorouk Academy, Cairo, 11837, Egypt
6 Department of Computer Engineering, Biruni University, Istanbul, 34010, Turkey
7 Mathematics Research Center, Near East University, Nicosia, 99138, Cyprus

* Corresponding Author: Anjan Biswas. Email:

Computer Modeling in Engineering & Sciences 2025, 142(3), 2513-2525. https://doi.org/10.32604/cmes.2025.062177

Received 12 December 2024; Accepted 23 January 2025; Issue published 03 March 2025

Abstract

Computational modeling plays a vital role in advancing our understanding and application of soliton theory. It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions. In the present study, we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity. This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures. The numerical simulation is accomplished through the application of an algorithm that integrates the classical Adomian method with the Laplace transform. The results obtained have not been previously reported for this type of nonlinearity. Additionally, for the purpose of comparison, the numerical examination has taken into account some scenarios with fixed parameter values. Notably, the numerical derivation of solitons without the assistance of an exact solution is an exceptional take-home lesson from this study. Furthermore, the proposed approach is demonstrated to possess optimal computational accuracy in the results presentation, which includes error tables and graphs. It is important to mention that the methodology employed in this study does not involve any form of linearization, discretization, or perturbation. Consequently, the physical nature of the problem to be solved remains unaltered, which is one of the main advantages.

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Keywords

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