Ukrainian Journal of Physical Optics


2024 Volume 25, Issue 3


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

SEQUEL TO "STATIONARY OPTICAL SOLITONS WITH NONLINEAR CHROMATIC DISPERSION FOR LAKSHMANAN-PORSEZIAN-DANIEL MODEL HAVING KERR LAW OF NONLINEAR REFRACTIVE INDEX": GENERALIZED TEMPORAL EVOLUTION

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
7Mathematics Research Center, Near East University, 99138 Nicosia, Cyprus
8Department of Computer Technical Engineering, Al-Rafidain University College, 10064 Baghdad, Iraq.

ABSTRACT

The current paper studies the Lakshmanan–Porsezian–Daniel equation with nonlinear chromatic dispersion and Kerr law of self–phase modulation having generalized temporal evolution. The governing model is analyzed using Lie symmetry. The implicit solution is in terms of Appell hypergeometric function. The parameter constraints of the solutions are also enumerated.

Keywords: quiescent solitons, Lie symmetry

UDC: 535.32

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    У цій статті досліджується рівняння Лакшманана–Порсезіана–Деніела з нелінійною хроматичною дисперсією та законом Керра самофазової модуляції, що має узагальнену часову еволюцію. Модель аналізується за допомогою симетрії Лі. Неявний розв’язок отримано в термінах гіпергеометричної функції Аппеля. Перераховані також обмеження параметрів рішень.

    Ключові слова: стаціонарні солітони, симетрія Лі

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