Ukrainian Journal of Physical Optics


2024 Volume 25, Issue 3


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

OPTICAL SOLITON PARAMETERS BY VARIATIONAL PRINCIPLE: POLYNOMIAL AND TRIPLE-POWER LAWS (SUPER-GAUSSONS AND SUPER-SECH PULSES)

1Reham M. A. Shohib, 2Mohamed E. M. Alngar, 3Ahmed H. Arnous, 4,5,6,7Anjan Biswas, 8Bharat Rawal, 9,10Yakup Yildirim, 11Seithuti P. Moshokoa and 5Ali Saleh Alshomrani

1Basic Science Department, Higher Institute of Foreign Trade & Management Sciences, New Cairo Academy, Cairo-379, Egypt
2Basic Science Department, Faculty of Computers and Artificial Intelligence, Modern University for Technology & Information, Cairo-11585, Egypt
3Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shoruk Academy, Cairo, Egypt
4Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245-2715, USA
5Mathematical 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
6Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati-800201, Romania
7Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, South Africa
8Department of Computer Science & Digital Technologies, Grambling State University, Grambling, LA 71245-2715, USA
9Department of Computer Engineering, Biruni University, Istanbul-34010, Turkey
10Mathematics Research Center, Near East University, 99138 Nicosia, Cyprus
11Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria-0008, South Africa

ABSTRACT

In this article, the parameter dynamics of super–Gaussian and super–sech pulses for the perturbed nonlinear Schrödinger’s equation with polynomial and triple–power nonlinearity laws are recovered. The variational principle successfully recovers this dynamical system.

Keywords: solitons, variational principle, perturbed nonlinear Schrodinger's equation, Euler-Lagrange equation

UDC: 535.32

    1. M. E. M. Alngar, R. M. A. Shohib, A. H. Arnous, A. Biswas, Y. Yildirim, A. J. M. Jawad & A. S. Alshomrani. "Optical soliton parameter dynamics by variational principle: parabolic and dual-power laws (super-Gaussian and super-sech pulses)". To appear in Journal of Applied Science and Engineering.
    2. Ayela, A. M., Edah, G., Elloh, C., Biswas, A., Ekici, M., Alzahrani, A. K., & Belic, M. R. (2021). Chirped super-Gaussian and super-sech pulse perturbation of nonlinear Schrödinger's equation with quadratic-cubic nonlinearity by variational principle. Physics Letters A, 396, 127231. doi:10.1016/j.physleta.2021.127231
    3. Ayela, A. M., Edah, G., Biswas, A., Zhou, Q., Yildirim, Y., Khan, S., Alzahrani, A. K. & Belic, M. R. (2022). Dynamical system of optical soliton parameters for anti-cubic and generalized anti-cubic nonlinearities with super-Gaussian and super-sech pulses. Optica Applicata, 52(1). doi:10.37190/oa220109
    4. 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
    5. Chen, Y. (1991). Variational principle for vector spatial solitons and nonlinear modes. Optics Communications, 84(5-6), 355-358. doi:10.1016/0030-4018(91)90102-J
    6. Diakonos, F. K., & Schmelcher, P. (2019). Super-Lagrangian and variational principle for generalized continuity equations. Journal of Physics A: Mathematical and Theoretical, 52(15), 155203. doi:10.1088/1751-8121/ab082f
    7. Ferreira, M. F. (2018). Variational approach to stationary and pulsating dissipative optical solitons. IET Optoelectronics, 12(3), 122-125. doi:10.1049/iet-opt.2017.0121

    У статті відновлено динаміку параметрів супер-гауссових і супер-секанс-гіперболічних імпульсів для збуреного нелінійного рівняння Шредінгера з поліноміальним і триступеневим законами нелінійності. Динамічна система відновлена за допомогою варіаційного принципу.

    Ключові слова: солітони, варіаційний принцип, збурене нелінійне рівняння Шредінгера, рівняння Ейлера–Лагранжа

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