Ukrainian Journal of Physical Optics


2024 Volume 25, Issue 1


ISSN 1609-1833 (Print)

OPTICAL SOLITONS FOR THE DISPERSIVE CONCATENATION MODEL BY LAPLACE-ADOMIAN DECOMPOSITION

1O. Gonzalez-Gaxiola, 2,3,4,5Anjan Biswas, 6,7Yakup Yildirim and 8Anwar Jaafar Mohamad Jawad

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, 34010 Istanbul, Turkey
7Department of Mathematics, Near East University, 99138 Nicosia, Cyprus
8Department of Computer Technical Engineering, Al-Rafidain University College, 10064 Baghdad, Iraq

ABSTRACT

This work numerically studies bright and dark optical solitons that emerge from the dispersive concatenation model, having the Kerr law of nonlinear refractive index, using the Laplace-Adomian decomposition scheme. The simulations, surface plots, and contour plots are presented. The error measure is observed to be infinitesimally small.

Keywords: solitons, Schrodinger equation, concatenation model, Adomian polynomials

UDC: 535.32

    1. Jawad, A. J. M., & Abu-AlShaeer, M. J. (2023). Highly dispersive optical solitons with cubic law and cubic-quinticseptic law nonlinearities by two methods. Al-Rafidain J. Eng. Sci., 1(1), 1-8. doi:10.61268/sapgh524
    2. Ankiewicz, A., & Akhmediev, N. (2014). Higher-order integrable evolution equation and its soliton solutions. Physics Letters A, 378(4), 358-361. doi:10.1016/j.physleta.2013.11.031
    3. Ankiewicz, A., Wang, Y., Wabnitz, S., & Akhmediev, N. (2014). Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions. Physical Review E, 89(1), 012907. doi:10.1103/PhysRevE.89.012907
    4. Chowdury, A., Kedziora, D. J., Ankiewicz, A., & Akhmediev, N. (2014). Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms. Physical Review E, 90(3), 032922. doi:10.1103/PhysRevE.90.032922
    5. Chowdury, A., Kedziora, D. J., Ankiewicz, A., & Akhmediev, N. (2015). Breather-to-soliton conversions described by the quintic equation of the nonlinear Schrödinger hierarchy. Physical Review E, 91(3), 032928. doi:10.1103/PhysRevE.91.032928
    6. Chowdury, A., Kedziora, D. J., Ankiewicz, A., & Akhmediev, N. (2015). Breather solutions of the integrable quintic nonlinear Schrödinger equation and their interactions. Physical Review E, 91(2), 022919. doi:10.1103/PhysRevE.91.022919
    7. Arnous, A. H., Mirzazadeh, M., Biswas, A., Yıldırım, Y., Triki, H., & Asiri, A. (2023). A wide spectrum of optical solitons for the dispersive concatenation model. Journal of Optics, 1-27. doi:10.1007/s12596-023-01383-8
    8. González-Gaxiola, O., Biswas, A., Ruiz de Chavez, J., & Asiri, A. (2023). Bright and dark optical solitons for the concatenation model by the Laplace-Adomian decomposition scheme. Ukrainian Journal of Physical Optics, 24(3), 222 - 234. doi:10.3116/16091833/24/3/222/2023
    9. Shohib Reham, M.A., Alngar Mohamed, E.M., Biswas, A., Yildirim, Y., Triki, H., Moraru, L., Catalina, I., Lucian, G.P. & Asiri, A. (2023). Optical solitons in magneto-optic waveguides for the concatenation model. Ukrainian Journal of Physical Optics, 24(3), 248 - 261. doi:10.3116/16091833/24/3/248/2023
    10. Biswas, A., Vega-Guzmán, J. M., Yildirim, Y., Moshokoa, S. P., Aphane, M., & Alghamdi, A. A. (2023). Optical solitons for the concatenation model with power-law nonlinearity: undetermined coefficients. Ukrainian Journal of Physical Optics, 24(3), 185 - 192. doi:10.3116/16091833/24/3/185/2023
    11. Biswas, A., Vega-Guzmán, J., Yildirim, Y., & Asiri, A. (2023). Optical Solitons for the Dispersive Concatenation Model: Undetermined Coefficients. Contemporary Mathematics, 951-961. doi:10.37256/cm.4420233618
    12. Zayed, E. M., Gepreel, K. A., El-Horbaty, M., Biswas, A., Yildirim, Y., Triki, H., & Asiri, A. (2023). Optical solitons for the dispersive concatenation model. Contemporary Mathematics, 592-611. doi:10.37256/cm.4320233321
    13. Adomian, G., & Rach, R. (1986). On the solution of nonlinear differential equations with convolution product nonlinearities. Journal of mathematical analysis and applications, 114(1), 171-175. doi:10.1016/0022-247X(86)90074-0
    14. Adomian, G. (2013). Solving frontier problems of physics: the decomposition method (Vol. 60). Springer Science & Business Media.
    15. Mohammed, A. S. H. F., & Bakodah, H. O. (2020). Numerical investigation of the Adomian-based methods with w-shaped optical solitons of Chen-Lee-Liu equation. Physica Scripta, 96(3), 035206. doi:10.1088/1402-4896/abd0bb
    16. Duan, J. S. (2011). Convenient analytic recurrence algorithms for the Adomian polynomials. Applied Mathematics and Computation, 217(13), 6337-6348. doi:10.1016/j.amc.2011.01.007

    У цій роботі чисельно досліджені світлі та темні оптичні солітони, які виникають із моделі дисперсійної конкатенації. В моделі закладено закон Керра для нелінійного показника заломлення з використанням схем розкладання Лапласа-Адоміана. В роботі представлено результати моделювання, поверхнями та двомірними графіками. Показано, що похибка є нескінченно малою.

    Ключові слова: солітони, рівняння Шредінгера, конкатенаційна модель, поліноми Адоміана

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