Journal of Applied Science and Engineering

Published by Tamkang University Press

1.30

Impact Factor

2.10

CiteScore

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.


Download Citation: ||https://doi.org/10.6180/jase.202410_27(10).0003  


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


  1. [1] R. Y. Chiao, E. Garmire, and C. H. Townes, (1964) “Self-trapping of optical beams" Physical review letters 13: 479. DOI: 10.1103/PhysRevLett.13.479.
  2. [2] P. Albayrak, M. Ozisik, M. Bayram, A. Secer, S. E. Das, A. Biswas, Y. Yıldırım, M. Mirzazadeh, and A. Asiri, (2023) “Pure-Cubic Optical Solitons and Stability Analysis with Kerr Law Nonlinearity" Contemporary Mathematics 4(3): 530–548. DOI: 10.37256/cm.4320233308.
  3. [3] D. Lu, A. R. Seadawy, J. Wang, M. Arshad, and U. Farooq, (2019) “Soliton solutions of the generalised thirdorder nonlinear Schrödinger equation by two mathematical methods and their stability" Pramana 93: 44. DOI: 10.1007/s12043-019-1804-5.
  4. [4] N. Nasreen, A. R. Seadawy, D. Lu, and W. A. Albarakati, (2019) “Dispersive solitary wave and soliton solutions of the gernalized third order nonlinear Schrödinger dynamical equation by modified analytical method" Results in Physics 15: 102641. DOI: 10.1016/j.rinp.2019.102641.
  5. [5] S. Malik, S. Kumar, K. S. Nisar, and C. A. Saleel, (2021) “Different analytical approaches for finding novel optical solitons with generalized third-order nonlinear Schrödinger equation" Results in Physics 29: 104755. DOI: 10.1016/j.rinp.2021.104755.
  6. [6] M. T. Islam, F. A. Abdullah, and J. Gómez-Aguilar, (2022) “A variety of solitons and other wave solutions of a nonlinear Schrödinger model relating to ultra-short pulses in optical fibers" Optical and Quantum Electronics 54: 866. DOI: 10.1007/s11082-022-04249-8.
  7. [7] H. M. Baskonus, M. Younis, M. Bilal, U. Younas, Shafqat-ur-Rehman, and W. Gao, (2020) “Modulation instability analysis and perturbed optical soliton and other solutions to the Gerdjikov-Ivanov equation in nonlinear optics" Modern Physics Letters B 34: 2050404. DOI: 10.1142/S0217984920504047.
  8. [8] J. Ahmad, S. Akram, S. U. Rehman, N. B. Turki, and N. A. Shah, (2023) “Description of soliton and lump solutions to M-truncated stochastic Biswas–Arshed model in optical communication" Results in Physics 51: 106719. DOI: 10.1016/j.rinp.2023.106719.
  9. [9] T. A. Sulaiman, U. Younas, M. Younis, J. Ahmad, S. U. Rehman, M. Bilal, and A. Yusuf, (2022) “Modulation instability analysis, optical solitons and other solutions to the (2+ 1)-dimensional hyperbolic nonlinear Schrodinger’s equation" Computational Methods for Differential Equations 10: 179–190. DOI: 10.22034/cmde.2020.38990.1711.
  10. [10] S. Rehman, M. Bilal, M. Inc, U. Younas, H. Rezazadeh, M. Younis, and S. Mirhosseini-Alizamini, (2022) “Investigation of pure-cubic optical solitons in nonlinear optics" Optical and Quantum Electronics 54: 400. DOI: 10.1007/s11082-022-03814-5.
  11. [11] J. K. Ghosh, P. Majumdar, and U. Ghosh, (2021) “Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment" Mathematical Modelling of Natural Phenomena 16: 13. DOI: 10.1051/mmnp/2021004.
  12. [12] K. Hosseini, M. Osman, M. Mirzazadeh, and F. Rabiei, (2020) “Investigation of different wave structures to the generalized third-order nonlinear Scrödinger equation" Optik 206: 164259. DOI: 10.1016/j.ijleo.2020.164259.
  13. [13] D. Zhao, D. Lu, and M. M. Khater, (2022) “Ultrashort pulses generation’s precise influence on the light transmission in optical fibers" Results in Physics 37: 105411. DOI: 10.1016/j.rinp.2022.105411.
  14. [14] G. Adomian and R. Rach, (1986) “On the solution of nonlinear differential equations with convolution product nonlinearities" Journal of mathematical analysis and applications 114: 171–175. DOI: 10.1016/0022-247X(86)90074-0.
  15. [15] G. Adomian. Solving frontier problems of physics: the decomposition method. Kluwer Academic Publishers, Boston MA, 1994.
  16. [16] J.-S. Duan, (2011) “Convenient analytic recurrence algorithms for the Adomian polynomials" Applied Mathematics and Computation 217: 6337–6348. DOI: 10.1016/j.amc.2011.01.007.
  17. [17] A.-M. Wazwaz, (2005) “Adomian decomposition method for a reliable treatment of the Emden–Fowler equation" Applied Mathematics and Computation 161: 543– 560. DOI: 10.1016/j.amc.2003.12.048.
  18. [18] J. Biazar and R. Islam, (2004) “Solution of wave equation by Adomian decomposition method and the restrictions of the method" Applied Mathematics and Computation 149: 807–814. DOI: 10.1016/S0096-3003(03)00186-3.


    



 

2.1
2023CiteScore
 
 
69th percentile
Powered by  Scopus

SCImago Journal & Country Rank

Enter your name and email below to receive latest published articles in Journal of Applied Science and Engineering.