Ukrainian Journal of Physical Optics


2024 Volume 25, Issue 2


ISSN 1609-1833 (Print)

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

1Abdullahi 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

The current paper extracts the implicit form of quiescent optical solitons that emerge from the nonlinear Schrödinger’s equation with the generalized form of quadratic–cubic nonlinear refractive index change. The work is with linear temporal evolution as well as with generalized temporal evolution. The results are in terms of Appell hypergeometric functions as in the case of the quadratic–cubic form of nonlinear refractive index, reported earlier. Lie symmetry analysis has made this retrieval possible.

Keywords: quiescent optical solitons, Lie symmetry

UDC: 535.32

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    У поточній роботі отримано неявну форму стаціонарних оптичних солітонів, які виникають з розв’язку нелінійного рівняння Шредінгера з узагальненою формою квадратично-кубічної нелінійної зміни показника заломлення. Дослідження проводиться як з лінійним часовим еволюційним процесом, так і з узагальненим часовим еволюційним процесом. Результати виражені через гіпергеометричні функції Аппеля, так само як у випадку квадратично-кубічної форми нелінійного показника заломлення, який був описаний раніше. Розв’язки отримані завдяки використанню симетрії Лі.

    Ключові слова: стаціонарні оптичні солітони, симетрія Лі

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