Ukrainian Journal of Physical Optics


2024 Volume 25, Issue 3


ISSN 1816-2002 (Online), ISSN 1609-1833 (Print)

OPTICAL SOLITONS FOR THE DISPERSIVE CONCATENATION MODEL WITH DIFFERENTIAL GROUP DELAY BY THE COMPLETE DISCRIMINANT APPROACH

1Ming-Yue Wang, 2,3,4,5Anjan Biswas, 6,7Yakup Yildirim, 4Maggie Aphane, 8Anwar Ja'afar Mohamad Jawad and 3Ali Saleh Alshomrani

1Key Laboratory of Mechanics on Disaster and Environment in Western China, The Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou-730000, China
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 Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, Pretoria, South Africa
5Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati-800201, Romania
6Department of Computer Engineering, Biruni University, Istanbul-34010, Turkey
7Mathematics Research Center, Near East University, 99138 Nicosia, Cyprus
8Department of Computer Technical Engineering, Al Rafidain University College, 10064 Baghdad, Iraq

ABSTRACT

The current paper recovers optical solitons for the dispersive concatenation model with polarization–mode dispersion. The complete discriminant approach has made this retrieval possible. The intermediary Jacobi’s elliptic functions gave way to the soliton solutions, with the limiting approach applied to such functions. These solitons are classified, and their surface and contour plots are sketched.

Keywords: concatenation model, solitons, dispersion, parameter constraints

UDC: 535.32

    1. 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
    2. 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
    3. 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
    4. 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
    5. 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
    6. Arnous, A. H., Biswas, A., Yildirim, Y., & Asiri, A. (2023). Quiescent optical solitons for the concatenation model having nonlinear chromatic dispersion with differential group delay. Contemporary Mathematics, 877-904. doi:10.37256/cm.4420233596
    7. Arnous, A. H., Anjan, B., Yakup, Y., Luminita, M., Catalina, I., Lucian, G. P., & Asim, A. (2023). Optical solitons and complexitons for the concatenation model in birefringent fibers. Ukrainian Journal of Physical Optics, 24(4), 04060–04086. doi:10.3116/16091833/24/4/04060/2023
    8. Arnous, A. H., Biswas, A., Kara, A. H., Yıldırım, Y., Moraru, L., Iticescu, C., Moldovanu, S. & Alghamdi, A. A. (2024). Optical solitons and conservation laws for the concatenation model: power-law nonlinearity. Ain Shams Engineering Journal, 15(2), 102381. doi:10.1016/j.asej.2023.102381
    9. Elsherbany, A. M., Arnous, A. H., Jawad, A. J. M., Biswas, A., Yildirim, Y., Moraru, L. & Alshomrani, A. S. (2024). Quiescent optical solitons for the dispersive concatenation model with Kerr law of nonlinearity having nonlinear chromatic dispersion. Ukrainian Journal of Physical Optics, 25(1), 01054-01064. doi:10.3116/16091833/Ukr.J.Phys.Opt.2024.01054
    10. A. H. Arnous, A. Biswas, A. H. Kara, Y. Yildirim & A. Asiri. "Optical solitons and conservation laws for the dispersive concatenation model with power-law nonlinearity". To appear in Journal of Optics. doi:10.1007/s12596-023-01453-x. https://doi.org/10.1007/s12596-023-01453-x
    11. 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
    12. Arnous, A. H., Biswas, A., Kara, A. H., Yıldırım, Y., Dragomir, C. M. B., & Asiri, A. (2023). Optical solitons and conservation laws for the concatenation model in the absence of self-phase modulation. Journal of Optics, 1-24. doi:10.1007/s12596-023-01392-7
    13. A. H. Arnous, A. Biswas, A. H. Kara, Y. Yıldırım, A. Asiri. "Optical solitons and conservation laws for the dispersive concatenation model with power-law nonlinearity". Journal of Optics. To appear in 10.1007/s12596-023-01453-x.
    14. Arnous, A. H., Biswas, A., Yildirim, Y., & Alshomrani, A. S. (2024). Stochastic Perturbation of Optical Solitons for the Concatenation Model with Power-Law of Self-Phase Modulation Having Multiplicative White Noise. Contemporary Mathematics, 567-589. doi:10.37256/cm.5120244107
    15. Vega-Guzmán, J., Biswas, A., Yıldırım, Y., & Alshomrani, A. S. (2024). Optical solitons for the dispersive concatenation model with power law of self-phase modulation: undetermined coefficients. Journal of Optics, 1-9. doi:10.1007/s12596-024-01697-1
    16. Arnous, A. H., Biswas, A., Yildirim, Y., Rawal, B. S., & Alshomrani, A. S. (2024). Optical solitons for the dispersive concatenation model with power law of self-phase modulation and multiplicative white noise. Journal of Optics, 1-12. doi:10.1007/s12596-024-01670-y
    17. Biswas, A., Vega-Guzman, 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
    18. 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
    19. Zayed, E. M., Arnous, A. H., Biswas, A., Yıldırım, Y., & Asiri, A. (2023). Optical solitons for the concatenation model with multiplicative white noise. Journal of Optics, 1-10. doi:10.1007/s12596-023-01381-w
    20. Jihad, N., & Abd Almuhsan, M. (2023). Evaluation of impairment mitigations for optical fiber communications using dispersion compensation techniques. Al-Rafidain Journal of Engineering Sciences, 81-92. doi:10.61268/0dat0751
    21. Arnous, A. H., Biswas, A., Yildirim Y. & Alshomrani, A. S. (2024). Optical solitons for the dispersive concatenation model with differential group delay. To appear in Nonlinear Optics, Quantum Optics: Concepts in Modern Optics.
    22. Cheng-Shi, L. I. U. (2006). Trial equation method to nonlinear evolution equations with rank inhomogeneous: mathematical discussions and its applications. Communications in Theoretical Physics, 45(2), 219–223. doi:10.1088/0253-6102/45/2/005
    23. Liu, C. S. (2011). Trial equation method based on symmetry and applications to nonlinear equations arising in mathematical physics. Foundations of Physics, 41, 793-804. doi:10.1007/s10701-010-9521-4
    24. Liu, C. S. (2005). Trial equation method and its applications to nonlinear evolution equations". Acta Physica Sinica. 54, 2505-2509. doi:10.7498/aps.54.2505
    25. Liu, C. S. (2005). New exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schrödinger equation. Communications in Theoretical Physics, 44(5), 799-801. doi:10.1088/6102/44/5/799
    26. Liu, C. S. (2010). Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations. Computer Physics Communications, 181(2), 317-324. doi:10.1016/j.cpc.2009.10.006

    У цій статті отримані розв’язки оптичних солітонів для моделі дисперсійної конкатенації з дисперсією поляризованої моди. Отримання результатів стало можливим завдяки використанню повного дискримінантного підходу. Проміжні еліптичні функції Якобі поступилися місцем солітонним розв’язкам із застосуванням до них граничних умов. В роботі класифіковані і зображені ці солітони.

    Ключові слова: concatenation model, solitons, dispersion, parameter constraints

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