Ukrainian Journal of Physical Optics


2023 Volume 24, Issue 1


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

Dark and singular cubic-quartic optical solitons with Lakshmanan-Porsezian-Daniel equation by the improved Adomian decomposition scheme

1Al Qarni A.A., 2Bodaqah A.M., 2Mohammed A.S.H.F., 2Alshaery A.A., 2Bakodah H.O. and 3,4,5,6Biswas A.

1Department of Mathematics, College of Science, University of Bisha, P. O. Box 551, Bisha-61922, Saudi Arabia
2Department of Mathematics, Faculty of Science, University of Jeddah, P. O. Box 80327, Jeddah, Saudi Arabia
3Department of Mathematics and Physics, Grambling State University, Grambling, LA-71245, USA
4Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah-21589, Saudi Arabia
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 Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, South Africa

ABSTRACT

We employ an enhanced version of a decomposition technique, an improved Adomian decomposition method, and confirm computationally its high accuracy for a number of dark and singular cubic–quartic optical solitons which arise from the Lakshmanan–Porsezian–Daniel equation. The overall recurrent scheme applied for the governing model is elucidated and further scrutinized with regard to the optical solitons mentioned above. The computational results are promising and reveal a remarkably high level of precision. Tables of the absolute errors and illustrating plots are provided to augment the main findings of our comparative study.

Keywords: computational methods, Lakshmanan-Porsezian-Daniel model, improved Adomian decomposition method, optical solitons, Kerr-law nonlinearity

UDC: 535.32

    1. Manukure S and Booker T, 2021. A short overview of solitons and applications. Partial Diff. Eq. Appl. Math. 4: 100140. doi:10.1016/j.padiff.2021.100140
    2. Zayed E M, Nofal T A, Gepreel K A, Shohib R and Alngar M E, 2021. Cubic-quartic optical soliton solutions in fiber Bragg gratings with Lakshmanan-Porsezian-Daniel model by two integration schemes. Opt. Quant. Electron. 53(5): 1-17. doi:10.1007/s11082-021-02907-x
    3. Biswas A, Triki H, Zhou Q, Moshokoa S P, Ullah M Z and Belic M, 2017. Cubic-quartic optical solitons in Kerr and power law media. Optik, 144: 357-362.‏‏ doi:10.1016/j.ijleo.2017.07.008
    4. Vega-Guzman J, Biswas A, Kara A H, Mahmood M F, Ekici M, Alshehri H M and Belic M R, 2021. Cubic-quartic optical soliton perturbation and conservation laws with Lakshmanan-Porsezian-Daniel model: Undetermined coefficients. J. Nonlin. Opt. Phys. Mater. 30(3-4): 2150007.‏ doi:10.1142/S0218863521500077
    5. Kumar S, Biswas A, Zhou Q, Yıldırım Y, Alshehri H M and Belic M R, 2021. Straddled optical solitons for cubic-quartic Lakshmanan-Porsezian-Daniel model by Lie symmetry. Phys. Lett. A. 417: 127706.‏ doi:10.1016/j.physleta.2021.127706
    6. Zayed E M, Alngar M E, Biswas A, Yıldırım Y, Khan S, Alzahrani A K and Belic M R, 2021. Cubic-quartic optical soliton perturbation in polarization-preserving fibers with Fokas-Lenells equation. Optik, 234: 166543. doi:10.1016/j.ijleo.2021.166543
    7. Zayed E M, Alngar M E, Biswas A, Yıldırım Y, Guggilla P, Khan S, Alzahrani A K and Belic M R, 2021. Cubic-quartic optical soliton perturbation with Lakshmanan-Porsezian-Daniel model. Optik, 233: 166385.‏ ‏doi:10.1016/j.ijleo.2021.166385
    8. Biswas A, Sonmezoglu A, Ekici M, Alzahrani A K and Belic M R, 2020. Cubic-quartic optical solitons with differential group delay for Kudryashov's model by extended trial function. J. Comm. Techn. Electr. 65(12): 1384-1398.‏ doi:10.1134/S1064226920120037
    9. Yıldırım Y, Topkara E, Biswas A, Triki H, Ekici M, Guggilla P, Khan S, & Belic M R, 2021. Cubic-quartic optical soliton perturbation with Lakshmanan-Porsezian-Daniel model by sine-Gordon equation approach. J. Opt. 50(2): 322-329.‏ doi:10.1007/s12596-021-00685-z
    10. Alzahrani A K and Belic M R, 2021. Cubic-quartic optical soliton perturbation with Lakshmanan-Porsezian--Daniel model by semi-inverse variational principle. Ukr. J. Phys. Opt. 22: 123.‏ doi:10.3116/16091833/22/3/123/2021
    11. Al Qarni A A, Bodaqah A M, Mohammed A S H F, Alshaery A A, Bakodah H O, and Biswas A, 2022, Cubic-quartic optical solitons for Lakshmanan-Porsezian-Daniel equation by the improved Adomian decomposition scheme. Ukr. J. Phys. Opt. 23(4): 228-242. doi:10.3116/16091833/23/4/228/2022
    12. Bakodah H O, Al Qarni A A, Banaja M A, Zhou Q, Moshokoa S P and Biswas A, 2017. Bright and dark Thirring optical solitons with improved Adomian decomposition method. Optik, 130: 1115-1123.‏ doi:10.1016/j.ijleo.2016.11.123
    13. Mohammed A S H F, Bakodah H O, Banaja M A, Alshaery A A, Zhou Q, Biswas A, Moshokoa S P & Belic M R, 2019. Bright optical solitons of Chen-Lee-Liu equation with improved Adomian decomposition method. Optik, 181: 964-970.‏ doi:10.1016/j.ijleo.2018.12.177
    14. Bakodah H O, Banaja M A, Alshaery A A and Al Qarni A A, 2019. Numerical solution of dispersive optical solitons with Schrödinger-Hirota equation by improved Adomian decomposition method. Math. Probl. Eng.‏ 2019: 2960912 doi:10.1155/2019/2960912
    15. Banaja M A, Al Qarni A A, Bakodah H O, Zhou Q, Moshokoa S P and Biswas A, 2017. The investigate of optical solitons in cascaded system by improved Adomian decomposition scheme. Optik, 130: 1107-1114.‏ doi:10.1016/j.ijleo.2016.11.125
    16. Al-Qarni A A, Bakodah H O, Alshaery A A, Biswas A, Yıldırım Y, Moraru L and Moldovanu S, 2022. Numerical simulation of cubic-quartic optical solitons with perturbed Fokas-Lenells equation using improved Adomian decomposition algorithm. Math. 10(1): 138.‏‏ doi:10.3390/math10010138
    17. Tang L, 2022. Bifurcations and dispersive optical solitons for the cubic-quartic nonlinear Lakshmanan-Porsezian-Daniel equation in polarization-preserving fibers. Optik. 270: 170000. doi:10.1016/j.ijleo.2022.170000
    18. Akram G, Sadaf M, Khan M A U, 2022. Soliton solutions of Lakshmanan-Porsezian-Daniel model using modified auxiliary equation method with parabolic and anti-cubic law of nonlinearities. Optik. 251: 168163. doi:10.1016/j.ijleo.2021.168163
    19. Bilal M, Younas U, Yusuf A, Sulaiman T A, Bayram M, 2021. Optical solitons with the birefringent fibers without four-wave mixing via the Lakshmanan-Porsezian-Daniel equation. Optik. 243: 167489. doi:10.1016/j.ijleo.2021.167489
    20. Kudryashov N A 2021. The Lakshmanan-Porsezian-Daniel model with arbitrary refractive index and its solution. Optik. 241: 167043. doi:10.1016/j.ijleo.2021.167043
    21. Xin H, 2021. Optical envelope patterns in nonlinear media modeled by the Lakshmanan-Porsezian-Daniel equation. Optik. 227: 165839. doi:10.1016/j.ijleo.2020.165839
    22. Yildirim Y, 2020. Optical soliton molecules of Lakshmanan-Porsezian-Daniel model in birefringent fibers by trial equation technique. Optik, 203: 162690. doi:10.1016/j.ijleo.2019.04.037
    23. Serkin V, Belyaeva T L, 2018. Optimal control for soliton breathers of the Lakshmanan-Porsezian-Daniel, Hirota, and cmKdV models. Optik, 175: 17-27. doi:10.1016/j.ijleo.2018.08.140

    Ми використали вдосконалену версію методу декомпозиції – покращений метод декомпозиції Адоміана – і чисельно підтвердили його високу точність для низки темних і сингулярних кубічно-квартичних оптичних солітонів, які з’являються з рівняння Лакшманана–Порсезіана–Даніеля. Пояснено загальну рекурентну схему, застосовану для керуючої математичної моделі, та додатково досліджено її на прикладі згаданих вище оптичних солітонів. Результати наших обчислень багатообіцяючі та демонструють надзвичайно високий рівень точності. Основні результати нашого порівняльного дослідження доповнено таблицями абсолютних похибок та ілюстраційними графіками.

    Ключові слова: обчислювальні методи, модель Лакшманана–Порсезіана–Деніела, удосконалений метод декомпозиції Адоміана, оптичні солітони, нелінійність за законом Керра

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