Ukrainian Journal of Physical Optics


2024 Volume 25, Issue 5


ISSN 1609-1833 (Print)

THREE EFFICIENT SCHEMES AND HIGHLY DISPERSIVE OPTICAL SOLITONS OF PERTURBED FOKAS-LENELLS EQUATION IN STOCHASTIC FORM

Y.Saglam Ozkan and E. Yasar

Department of Mathematics, Bursa Uludag University, Turkey

ABSTRACT

We contemplate a highly dispersive stochastic perturbed Fokas–Lenells model for fiber Bragg gratings with spatiotemporal dispersion and generated white noise in the Itô meaning. To acquire soliton solutions, we pertain to an exp(-f(ξ))-expansion method, a (G/G')-expansion technique and a simplest-equation method. 3D and 2D plots are built to make the wave-propagation behavior clear. The solitons of different kinds obtained by us like dark, singular, periodic, rational and combined solitons are compared with each other. The efficiency of our methods for the underlying model is evaluated.

Keywords: Fokas-Lenells model, exp(-f(ξ))-expansion method, (G/G')-expansion method, the simplest-equation method, solitons

UDC: 535.32

    1. Fu, L., Li, J., Yang, H., Dong, H., & Han, X. (2023). Optical solitons in birefringent fibers with the generalized coupled space-time fractional non-linear Schrödinger equations. Frontiers in Physics, 11, 1108505. doi:10.3389/fphy.2023.1108505
    2. 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
    3. Wang, S. (2023). Novel soliton solutions of CNLSEs with Hirota bilinear method. Journal of Optics, 1-6. doi:10.1007/s12596-022-01065-x
    4. 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
    5. Thi, T. N., & Van, L. C. (2023). Supercontinuum generation based on suspended core fiber infiltrated with butanol. Journal of Optics, 1–10. doi:10.1007/s12596-023-01323-6
    6. 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
    7. Jhangeer, A., Faridi, W. A., Asjad, M. I., & Akgül, A. (2021). Analytical study of soliton solutions for an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics by an expansion algorithm. Partial Differential Equations in Applied Mathematics, 4, 100102. doi:10.1016/j.padiff.2021.100102
    8. 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
    9. 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
    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. Kaplan, M., Hosseini, K., Samadani, F., & Raza, N. (2018). Optical soliton solutions of the cubic-quintic non-linear Schrödinger’s equation including an anti-cubic term. Journal of Modern Optics, 65(12), 1431–1436. doi:10.1080/09500340.2018.1442509
    12. 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
    13. 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
    14. 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
    15. Rehman, S. U., Seadawy, A. R., Younis, M., Rizvi, S. T., Sulaiman, T. A., & Yusuf, A. (2021). Modulation instability analysis and optical solitons of the generalized model for description of propagation pulses in optical fiber with four non-linear terms. Modern Physics Letters B, 35(06), 2150112. doi:10.1142/S0217984921501128
    16. 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
    17. 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
    18. 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
    19. Ahmad, S., Salman, Ullah, A., Ahmad, S., & Akgül, A. (2023). Bright, dark and hybrid multistrip optical soliton solutions of a non-linear Schrödinger equation using modified extended tanh technique with new Riccati solutions. Optical and Quantum Electronics, 55(3), 236. doi:10.1007/s11082-022-04490-1
    20. 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
    21. Jawad, A., & Abu-AlShaeer, M. (2023). Highly dispersive optical solitons with cubic law and cubic-quintic-septic law nonlinearities by two methods. Al-Rafidain Journal of Engineering Sciences, 1–8.
    22. Arnous, A. H., & Moraru, L. (2022). Optical solitons with the complex Ginzburg–Landau equation with Kudryashov’s law of refractive index. Mathematics, 10(19), 3456. doi:10.3390/math10193456
    23. Kopçasız, B., Seadawy, A. R., & Yaşar, E. (2022). Highly dispersive optical soliton molecules to dual-mode nonlinear Schrödinger wave equation in cubic law media. Optical and Quantum Electronics, 54(3), 194. doi:10.1007/s11082-022-03561-7
    24. Ozisik, M., Secer, A., & Bayram, M. (2022). On the examination of optical soliton pulses of Manakov system with auxiliary equation technique. Optik, 268, 169800. doi:10.1016/j.ijleo.2022.169800
    25. Savescu, M., Alkhateeb, S. A., Banaja, M. A., Alshaery, A. A., Hilal, E. M., Milovic, D., & Biswas, A. (2016). Thirring solitons in optical fibers with parabolic law nonlinearity. Journal of Computational and Theoretical Nanoscience, 13(7), 4656–4659. doi:10.1166/jctn.2016.5332
    26. Zayed, E. M., Gepreel, K. A., & El-Horbaty, M. (2023). Highly dispersive optical solitons in fiber Bragg gratings with stochastic perturbed Fokas–Lenells model having spatio-temporal dispersion and multiplicative white noise. Optik, 286, 170975. doi:10.1016/j.ijleo.2023.170975
    27. Zayed, E. M., Gepreel, K. A., El-Horbaty, M., & Alngar, M. E. (2023). Highly dispersive optical solitons in birefringent fibers of complex Ginzburg–Landau equation of sixth order with Kerr law nonlinear refractive index. Eng., 4(1), 665–677. doi:10.3390/eng4010040
    28. Kudryashov, N. A. (2012). One method for finding exact solutions of nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation, 17(6), 2248–2253. doi:10.1016/j.cnsns.2011.10.016
    29. Kudryashov, N. A. (2019). A generalized model for description of propagation pulses in optical fiber. Optik, 189, 42–52. doi:10.1016/j.ijleo.2019.05.069
    30. Kudryashov, N. A., & Antonova, E. V. (2020). Solitary waves of equation for propagation pulse with power nonlinearities. Optik, 217, 164881. doi:10.1016/j.ijleo.2020.164881
    31. Akram, G., & Mahak, N. (2018). Application of the first integral method for solving (1+ 1) dimensional cubic-quintic complex Ginzburg–Landau equation. Optik, 164, 210–217. doi:10.1016/j.ijleo.2018.02.108
    32. Zayed, E. M., Alngar, M. E., Biswas, A., Asma, M., Ekici, M., Alzahrani, A. K., & Belic, M. R. (2020). Pure-cubic optical soliton perturbation with full nonlinearity by unified Riccati equation expansion. Optik, 223, 165445. doi:10.1016/j.ijleo.2020.165445
    33. Zayed, E. M., Alngar, M. E., El-Horbaty, M., Biswas, A., Alshomrani, A. S., Khan, S., Ekici, M. & Triki, H. (2020). Optical solitons in fiber Bragg gratings having Kerr law of refractive index with extended Kudryashov’s method and new extended auxiliary equation approach. Chinese Journal of Physics, 66, 187–205. doi:10.1016/j.cjph.2020.04.003
    34. Biswas, A., Yıldırım, Y., Yaşar, E., Zhou, Q., Alshomrani, A. S., Moshokoa, S. P., & Belic, M. (2018). Solitons for perturbed Gerdjikov–Ivanov equation in optical fibers and PCF by extended Kudryashov’s method. Optical and Quantum Electronics, 50, 1–13. doi:10.1007/s11082-018-1417-0
    35. Gepreel, K. A., Zayed, E. M. E., & Alngar, M. E. M. (2021). New optical solitons perturbation in the birefringent fibers for the CGL equation with Kerr law nonlinearity using two integral schemes methods. Optik, 227, 166099. doi:10.1016/j.ijleo.2020.166099
    36. Zayed, E. M., Alngar, M. E., & Al-Nowehy, A. G. (2019). On solving the nonlinear Schrödinger equation with an anti-cubic nonlinearity in presence of Hamiltonian perturbation terms. Optik, 178, 488–508. doi:10.1016/j.ijleo.2018.09.064
    37. Biswas, A., Ekici, M., Triki, H., Sonmezoglu, A., Mirzazadeh, M., Zhou, Q., Mahmood, M., Zaka, Ul- lahi M., Moshokoam, S. & Belic, M. (2018). Resonant optical soliton perturbation with anti-cubic nonlinearity by extended trial function method. Optik, 156, 784–790. doi:10.1016/j.ijleo.2017.12.035
    38. Zayed, E. M., Shohib, R. M., Alngar, M. E., & Yıldırım, Y. (2021). Optical solitons in fiber Bragg gratings with Radhakrishnan–Kundu–Lakshmanan equation using two integration schemes. Optik, 245, 167635. doi:10.1016/j.ijleo.2021.167635
    39. Tian, S. F., & Zhang, T. T. (2018). Long-time asymptotic behavior for the Gerdjikov–Ivanov type of derivative nonlinear Schrödinger equation with time-periodic boundary condition. Proceedings of the American Mathematical Society, 146(4), 1713–1729. doi:10.1090/proc/13917
    40. Bowers, J., & Chou, H. F. (2005). Optical Communication Systems. Wavelength Division Multiplexing. Elsevier. doi:10.1016/B0-12-369395-0/00673-4
    41. Blanco-Redondo, A., De Sterke, C. M., Sipe, J. E., Krauss, T. F., Eggleton, B. J., & Husko, C. (2016). Pure-quartic solitons. Nature Communications, 7(1), 10427. doi:10.1038/ncomms10427
    42. Triki, H., Pan, A., & Zhou, Q. (2023). Pure-quartic solitons in presence of weak nonlocality. Physics Letters A, 459, 128608. doi:10.1016/j.physleta.2022.128608
    43. Zayed, E. M., Gepreel, K. A., El-Horbaty, M., Biswas, A., Yıldırım, Y., & Alshehri, H. M. (2021). Highly dispersive optical solitons with complex Ginzburg–Landau equation having six nonlinear forms. Mathematics, 9(24), 3270. doi:10.3390/math9243270
    44. Kudryashov, N. A. (2005). Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos, Solitons & Fractals, 24(5), 1217–1231. doi:10.1016/j.chaos.2004.09.109
    45. Roshid, H. O., Kabir, M. R., Bhowmik, R. C., & Datta, B. K. (2014). Investigation of Solitary wave solutions for Vakhnenko–Parkes equation via exp-function and Exp(−ϕ(ξ))-expansion method. SpringerPlus, 3(1), 1–10. doi:10.1186/2193-1801-3-692
    46. Kudryashov, N. A. (2005). Exact solitary waves of the Fisher equation. Physics Letters A, 342(1–2), 99–106. doi:10.1016/j.physleta.2005.05.025
    47. Wang, M., Li, X., & Zhang, J. (2008). The (G′/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A, 372(4), 417–423. doi:10.1016/j.physleta.2007.07.051
    48. Bekir, A. (2008). Application of the (G′/G)-expansion method for nonlinear evolution equations. Physics Letters A, 372(19), 3400–3406. doi:10.1016/j.physleta.2008.01.057
    49. Rezazadeh, H., Davodi, A. G., & Gholami, D. (2023). Combined formal periodic wave-like and soliton-like solutions of the conformable Schrödinger-KdV equation using the G′/G-expansion technique. Results in Physics, 47, 106352. doi:10.1016/j.rinp.2023.106352

    Розглянуто високодисперсійну стохастичну збурену модель Фокаса–Ленелля для волоконних бреггівських ґраток із просторово-часовою дисперсією та генерованим білим шумом у розумінні Іто. Для одержання солітонних рішень використано метод exp(-f(ξ))-розкладу, метод (G/G')-розкладу та метод найпростішого рівняння. Для ліпшого розуміння характеру розповсюдження хвиль побудовано тривимірні та двовимірні графіки. Виконано порівняння одержаних солітонів різних типів, таких як темні, сингулярні, періодичні, раціональні та комбіновані солітони. Оцінено ефективність наших методів для базової моделі.

    Ключові слова: високодисперсійна стохастична збурена модель Фокаса–Ленеллса, метод exp(-f(ξ))-розкладу, метод (G/G')-розкладу, метод найпростіших рівнянь, солітони

Free download this article 

© Ukrainian Journal of Physical Optics ©