Ukrainian Journal of Physical Optics


2024 Volume 25, Issue 5


ISSN 1609-1833 (Print)

Quiescent Optical Solitons for Fokas-Lenells Equation with Nonlinear Chromatic Dispersion Having Quadratic and Quadratic-Quartic Forms of Self-Phase Modulation

1,2Yakup Yildirim

1Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey
2Department of Mathematics, Near East University, 99138 Nicosia, Cyprus.

ABSTRACT

Quiescent optical soliton solutions within the Fokas-Lenells equation, accounting for nonlinear chromatic dispersion, are being investigated in this study for the first time. Two forms of self-phase modulation, quadratic and quadratic-quartic, are considered, including perturbation terms to introduce added complexity that refers to the inclusion of perturbation terms in the analysis of self-phase modulation. The F-expansion integration method is employed for finding various soliton solutions, including bright, dark, and singular solitons. These solitons are characterized by specific features that are influenced by their behavior.

Keywords: perturbed Fokas-Lenells equation, nonlinear chromatic dispersion, quiescent optical soliton, F-expansion method

UDC: 535.32

    1. Al-Ghafri, K. S., Sankar, M., Krishnan, E. V., Khan, S., & Biswas, A. (2023). Chirped gap solitons in fiber Bragg gratings with polynomial law of nonlinear refractive index. Journal of the European Optical Society, 19(1). doi:10.1051/jeos/2023025
    2. Al-Ghafri, K. S., Krishnan, E. V., & Biswas, A. (2022). Cubic-quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas-Lenells equation. Journal of the European Optical Society-Rapid Publications, 18(2), 9. doi:10.1051/jeos/2022008
    3. Topkara, E., Milovic, D., Sarma, A., Majid, F., & Biswas, A. (2009). A study of optical solitons with Kerr and power law nonlinearities by He's variational principle. Journal of the European Optical Society-Rapid Publications, 4. doi:10.2971/jeos.2009.09050
    4. González-Gaxiola, O., Biswas, A., & Belic, M. R. (2019). Optical soliton perturbation of Fokas-Lenells equation by the Laplace-Adomian decomposition algorithm. Journal of the European Optical Society-Rapid Publications, 15, 1-9. doi:10.1186/s41476-019-0111-6
    5. Arnous, A. H., Biswas, A., Kara, A. H., Yıldırım, Y., Moraru, L., Iticescu, C., Moldovanu, S., & Alghamdi, A. A. (2023). Optical solitons and conservation laws for the concatenation model with spatio-temporal dispersion (internet traffic regulation). Journal of the European Optical Society-Rapid Publications, 19(2), 35. doi:10.1051/jeos/2023031
    6. Zayed, E. M., El-Horbaty, M., Alngar, M. E., Shohib, R. M., Biswas, A., Yıldırım, Y., Moraru, L., Iticescu, C., Bibicu, D., Georgescu, P. L., & Asiri, A. (2023). Dynamical system of optical soliton parameters by variational principle (super-Gaussian and super-sech pulses). Journal of the European Optical Society-Rapid Publications, 19(2), 38. doi:10.1051/jeos/2023035
    7. Biswas, A. (2020). Optical soliton cooling with polynomial law of nonlinear refractive index. Journal of Optics, 49(4), 580-583. doi:10.1007/s12596-020-00644-0
    8. Wang, S. (2023). Novel soliton solutions of CNLSEs with Hirota bilinear method. Journal of Optics, 1-6. doi:10.1007/s12596-022-01065-x
    9. Han, T., Li, Z., Li, C., & Zhao, L. (2023). Bifurcations, stationary optical solitons and exact solutions for complex Ginzburg-Landau equation with nonlinear chromatic dispersion in non-Kerr law media. Journal of Optics, 52(2), 831-844. doi:10.1007/s12596-022-01041-5
    10. 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
    11. Chen, W., Shen, M., Kong, Q., & Wang, Q. (2015). The interaction of dark solitons with competing nonlocal cubic nonlinearities. Journal of Optics, 44, 271-280. doi:10.1007/s12596-015-0255-8
    12. Xu, S. L., Petrović, N., & Belić, M. R. (2015). Two-dimensional dark solitons in diffusive nonlocal nonlinear media. Journal of Optics, 44, 172-177. doi:10.1007/s12596-015-0243-z
    13. Dowluru, R. K., & Bhima, P. R. (2011). Influences of third-order dispersion on linear birefringent optical soliton transmission systems. Journal of Optics, 40, 132-142. doi:10.1007/s12596-011-0045-x
    14. Singh, M., Sharma, A. K., & Kaler, R. S. (2011). Investigations on optical timing jitter in dispersion managed higher order soliton system. Journal of Optics, 40, 1-7. doi:10.1007/s12596-010-0021-x
    15. Janyani, V. (2008). Formation and Propagation-Dynamics of Primary and Secondary Soliton-Like Pulses in Bulk Nonlinear Media. Journal of Optics, 37, 1-8. doi:10.1007/BF03354831
    16. Hasegawa, A. (2004). Application of Optical Solitons for Information Transfer in Fibers-A Tutorial Review. Journal of Optics, 33(3), 145-156. doi:10.1007/BF03354760
    17. Mahalingam, A., Uthayakumar, A., & Anandhi, P. (2013). Dispersion and nonlinearity managed multisoliton propagation in an erbium doped inhomogeneous fiber with gain/loss. Journal of Optics, 42, 182-188. doi:10.1007/s12596-012-0105-x
    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. doi:10.61268/sapgh524
    19. Triki, H., Zhou, Q., Biswas, A., Liu, W., Yıldırım, Y., Alshehri, H. M., & Belic, M. R. (2022). Localized pulses in optical fibers governed by perturbed Fokas-Lenells equation. Physics Letters A, 421, 127782. doi:10.1016/j.physleta.2021.127782
    20. Triki, H., Zhou, Q., Liu, W., Biswas, A., Moraru, L., Yıldırım, Y., Alshehri, H. M., & Belic, M. R. (2022). Chirped optical soliton propagation in birefringent fibers modeled by coupled Fokas-Lenells system. Chaos, Solitons & Fractals, 155, 111751. doi:10.1016/j.chaos.2021.111751
    21. Triki, H., & Wazwaz, A. M. (2017). Combined optical solitary waves of the Fokas-Lenells equation. Waves in Random and Complex Media, 27(4), 587-593. doi:10.1080/17455030.2017.1285449
    22. Triki, H., & Wazwaz, A. M. (2017). New types of chirped soliton solutions for the Fokas-Lenells equation. International Journal of Numerical Methods for Heat & Fluid Flow, 27(7), 1596-1601. doi:10.1108/HFF-06-2016-0252
    23. Bansal, A., Kara, A. H., Biswas, A., Khan, S., Zhou, Q., & Moshokoa, S. P. (2019). Optical solitons and conservation laws with polarization-mode dispersion for coupled Fokas-Lenells equation using group invariance. Chaos, Solitons & Fractals, 120, 245-249. doi:10.1016/j.chaos.2019.01.030
    24. Li, Z., & Huang, C. (2023). Bifurcation, phase portrait, chaotic pattern and optical soliton solutions of the conformable Fokas-Lenells model in optical fibers. Chaos, Solitons & Fractals, 169, 113237. doi:10.1016/j.chaos.2023.113237
    25. Wang, B. H., Wang, Y. Y., Dai, C. Q., & Chen, Y. X. (2020). Dynamical characteristic of analytical fractional solitons for the space-time fractional Fokas-Lenells equation. Alexandria Engineering Journal, 59(6), 4699-4707. doi:10.1016/j.aej.2020.08.027
    26. Wang, Z., He, L., Qin, Z., Grimshaw, R., & Mu, G. (2019). High-order rogue waves and their dynamics of the Fokas-Lenells equation revisited: a variable separation technique. Nonlinear Dynamics, 98, 2067-2077. doi:10.1007/s11071-019-05308-8
    27. Li, Z., Fan, W., & Miao, F. (2023). Chaotic pattern, phase portrait, sensitivity and optical soliton solutions of coupled conformable fractional Fokas-Lenells equation with spatio-temporal dispersion in birefringent fibers. Results in Physics, 47, 106386. doi:10.1016/j.rinp.2023.106386
    28. Yıldırım, Y., Biswas, A., Moraru, L., & Alghamdi, A. A. (2023). Quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion. Mathematics, 11(7), 1709. doi:10.3390/math11071709
    29. Yıldırım, Y., & Mirzazadeh, M. (2020). Optical pulses with Kundu-Mukherjee-Naskar model in fiber communication systems. Chinese Journal of Physics, 64, 183-193. doi:10.1016/j.cjph.2019.10.025
    30. Yıldırım, Y., Biswas, A., Kara, A. H., Ekici, M., Alzahrani, A. K., & Belic, M. R. (2021). Cubic-quartic optical soliton perturbation and conservation laws with generalized Kudryashov's form of refractive index. Journal of Optics, 50, 354-360. doi:10.1007/s12596-021-00681-3

    У цьому дослідженні вперше розглядаються розв'язки стаціонарних оптичних солітонів в межах рівняння Фокаса-Ленеллса з урахуванням нелінійної хроматичної дисперсії. Розглянуто дві форми самомодуляції фази - квадратична та квадратично-квартична, з включенням членів збурення для введення додаткової складності, яка стосується включення членів збурення в аналізі самомодуляції фази. Використовується метод інтегрування F-розкладу для знаходження різних розв'язків солітонів, включаючи яскраві, темні та сингулярні солітони. Ці солітони характеризуються певними особливостями, які визначають їхню поведінку.

    Ключові слова: збурене рівняння Фокаса–Ленеллса, нелінійна хроматична дисперсія, стаціонарний оптичний солітон, метод F-розкладу

Free download this article 

© Ukrainian Journal of Physical Optics ©