Ukrainian Journal of Physical Optics


2024 Volume 25, Issue 2


ISSN 1609-1833 (Print)

IMPLICIT QUIESCENT OPTICAL SOLITONS FOR COMPLEX GINZBURG-LANDAU EQUATION WITH GENERALIZED QUADRATIC-CUBIC FORM OF SELF-PHASE MODULATION AND NONLINEAR CHROMATIC DISPERSION BY LIE SYMMETRY

1`Abdullahi Rashid Adem, 2,3,4,5Anjan Biswas, 6,7Yakup Yildirim, 8Anwar Jaafar Mohamad Jawad and 3Ali Saleh Alshomrani

1Department of Mathematical Sciences, University of South Africa, UNISA-0003, South Africa
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, South Africa
6Department of Computer Engineering, Biruni University, Istanbul-34010, 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 is on the retrieval of quiescent optical solitons for the complex Ginzburg–Landau equation that is with nonlinear chromatic dispersion and generalized structure of quadratic–cubic form of self–phase modulation. The Lie symmetry is applied to make this retrieval possible. The model is studied with linear temporal evolutions as well as generalized temporal evolution.

Keywords: quiescent solitons, Lie symmetry

UDC: 535.32

    1. Adem, A. R., Biswas, A., Yıldırım, Y., & Asiri, A. (2023). Implicit quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion and power-law of self-phase modulation by Lie symmetry. Journal of Optics, 1-6. doi:10.1007/s12596-023-01443-z
    2. Adem, A. R., Biswas, A., Yıldırım, Y., & Asiri, A. (2023). Implicit quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion and in absence of self-phase modulation by Lie symmetry. Journal of Optics,. doi:10.1007/s12596-023-01451-z
    3. Adem, A. R., Biswas, A., Yildirim, Y., & Asiri, A. (2023). Implicit Quiescent Optical Solitons for the Dispersive Concatenation Model with Nonlinear Chromatic Dispersion by Lie Symmetry. Contemporary Mathematics, 666-674. doi:10.37256/cm.4420233575
    4. Adem, A. R., Ntsime, B. P., Biswas, A., Asma, M., Ekici, M., Moshokoa, S. P., Alzahrani, A. K. & Belic, M. R. (2020). Stationary optical solitons with Sasa-Satsuma equation having nonlinear chromatic dispersion. Physics Letters A, 384(27), 126721. doi:10.1016/j.physleta.2020.126721
    5. Adem, A. R., Ekici, M., Biswas, A., Asma, M., Zayed, E. M., Alzahrani, A. K., & Belic, M. R. (2020). Stationary optical solitons with nonlinear chromatic dispersion having quadratic-cubic law of refractive index. Physics Letters A, 384(25), 126606. doi:10.1016/j.physleta.2020.126606
    6. Adem, A. R., Ntsime, B. P., Biswas, A., Khan, S., Alzahrani, A. K., & Belic, M. R. (2021). Stationary optical solitons with nonlinear chromatic dispersion for Lakshmanan-Porsezian-Daniel model having Kerr law of nonlinear refractive index. Ukrainian Journal of Physical Optics, 22(2), 83-86. doi:10.3116/16091833/22/2/83/2021
    7. Adem, A. R., Ntsime, B. P., Biswas, A., Dakova, A., Ekici, M., Yidirim, Y., & Alshehri, H. M. (2022). Stationary optical solitons with Kudryashov's self-phase modulation and nonlinear chromatic dispersion. Optoelectronics and Advanced Materials-Rapid Communications, 16(January-February 2022), 58-60.
    8. Adem, A. R., Ntsime, B. P., Biswas, A. N. J. A. N., Ekici, M., Yildirim, Y. A. K. U. P., & Alshehri, H. M. (2022). Implicit quiescent optical solitons with complex Ginzburg-Landau equation having nonlinear chromatic dispersion. Journal of Optoelectronics and Advanced Materials, 24(September-October 2022), 450-462.
    9. Adem, A. R., Biswas, A., Yildirim, Y., Jawad, A. J. M., & Alshomrani, A. S. (2024). Implicit quiescent optical solitons with generalized quadratic–cubic form of self–phase modulation and nonlinear chromatic dispersion by Lie symmetry. Ukrainian Journal of Physical Optics, 25(5), 02016 – 02020, 10.3116/16091833/Ukr.J.Phys.Opt.2024.02016
    10. Biswas, A., & Khalique, C. M. (2011). Stationary solutions for nonlinear dispersive Schrödinger's equation. Nonlinear Dynamics, 63, 623-626. doi:10.1007/s11071-010-9824-1
    11. Biswas, A., & Khalique, C. M. (2013). Stationary solutions for the nonlinear dispersive Schrödinger equation with generalized evolution. Chinese Journal of Physics, 51(1), 103-110.
    12. Yan, Z. (2006). Envelope compactons and solitary patterns. Physics Letters A, 355(3), 212-215. doi:10.1016/j.physleta.2006.02.032
    13. Yan, Z. (2006). Envelope compact and solitary pattern structures for the GNLS (m, n, p, q) equations. Physics Letters A, 357(3), 196-203. doi:10.1016/j.physleta.2006.04.032
    14. Li, Z., & Zhu, E. (2023). Optical soliton solutions of stochastic Schrödinger-Hirota equation in birefringent fibers with spatiotemporal dispersion and parabolic law nonlinearity. Journal of Optics, 1-7. doi:10.1007/s12596-023-01287-7
    15. Devika, V., Mani Rajan, M. S., Thenmozhi, H., & Sharaf, A. (2023). Flower core photonic crystal fibres for supercontinuum generation with low birefringent structure for biomedical imaging. Journal of Optics, 52(2), 539-547. doi:10.1007/s12596-022-01002-y
    16. Mani Rajan, M. S. (2016). Dynamics of optical soliton in a tapered erbium-doped fiber under periodic distributed amplification system. Nonlinear Dynamics, 85(1), 599-606. doi:10.1007/s11071-016-2709-1
    17. Manirajan, M. S & Seyezhai, R. (2016). Capacitor voltage balancing control for modular multilevel cascaded inverter based on phase shifted pulse width modulation technique. Advances in Natural and Applied Sciences, 10(3), 205-215.
    18. 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.
    19. Nandy, S., & Lakshminarayanan, V. (2015). Adomian decomposition of scalar and coupled nonlinear Schrödinger equations and dark and bright solitary wave solutions. Journal of Optics, 44, 397-404. doi:10.1007/s12596-015-0270-9
    20. Tang, L. (2023). Bifurcations and optical solitons for the coupled nonlinear Schrödinger equation in optical fiber Bragg gratings. Journal of Optics, 52(3), 1388-1398. doi:10.1007/s12596-022-00963-4
    21. Tang, L. (2023). Phase portraits and multiple optical solitons perturbation in optical fibers with the nonlinear Fokas-Lenells equation. Journal of Optics, 1-10. doi:10.1007/s12596-023-01097-x
    22. Wang, T. Y., Zhou, Q., & Liu, W. J. (2022). Soliton fusion and fission for the high-order coupled nonlinear Schrödinger system in fiber lasers. Chinese Physics B, 31(2), 020501. doi:10.1088/1674-1056/ac2d22
    23. Zhong, Y., Triki, H., & Zhou, Q. (2023). Analytical and numerical study of chirped optical solitons in a spatially inhomogeneous polynomial law fiber with parity-time symmetry potential. Communications in Theoretical Physics, 75(2), 025003. doi:10.1088/1572-9494/aca51c
    24. Zhou, Q. (2022). Influence of parameters of optical fibers on optical soliton interactions. Chinese Physics Letters, 39(1), 010501. doi:10.1088/0256-307X/39/1/010501

    Ця робота присвячена отриманню стаціонарних оптичних солітонів для комплексного рівняння Гінзбурга–Ландау з нелінійною хроматичною дисперсією та узагальненою структурою квадратично-кубічної форми самомодуляції фази. Для досягнення цього використовується симетрія Лі. Модель досліджується з лінійною часовою еволюцією, а також з узагальненою часовою еволюцією.

    Ключові слова: спокійні солітони, симетрія Лі

Free download this article 

© Ukrainian Journal of Physical Optics ©