Ukrainian Journal of Physical Optics


2024 Volume 25, Issue 2


ISSN 1609-1833 (Print)

CUBIC-QUARTIC OPTICAL SOLITONS WITH KUDRYASHOV'S LAW OF SELF-PHASE MODULATION

Khalil S. Al-Ghafri1, Edamana V. Krishnan2, Anjan Biswas3,4,5,6, Yakup Yildirim7,8 and Ali Saleh Alshomrani4

1University of Technology and Applied Sciences, P.O. Box 14, Ibri 516, Oman
2Department of Mathematics, Sultan Qaboos University, P.O. Box 36, Al-Khod, Muscat 123, Oman
3Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245-2715, USA
4Mathematical 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
5Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201 Galati, Romania
6Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, Pretoria, South Africa
7Department of Computer Engineering, Biruni University, Istanbul, 34010, Turkey
8Department of Mathematics, Near East University, 99138, Nicosia, Cyprus

ABSTRACT

This study aims to investigate cubic-quartic optical solitons with Kudryashov’s law of self-phase modulation. Thus, the combination of third-order dispersion (3OD) and fourth-order dispersion (4OD) is assumed in the model to ensure the smooth existence of solitons. The study is implemented with the aid of two effective integration schemes known as the improved projective Riccati equations method and the soliton ansatz technique. The soliton solutions are derived based on two physical cases targeting the relation between 3OD and 4OD. In case 3OD is equivalent to fourfold frequency times 4OD, only dark and singular soliton profiles are extracted. However, if the former relation is not achieved, various structures of soliton pulses are generated, including kink-dark, singular, W-shaped, bright, dark, kink, and anti-kink solitons. The physical interpretations of retrieved optical solitons are represented by illustrating the wave behaviors with suitable values of model parameters. The results show that the combination of 3OD and 4OD has a significant effect on the dynamics of soliton propagation.

Keywords: optical solitons, cubic-quartic dispersion, Kudryashov's law, improved projective Riccati equations method, soliton ansatz

UDC: 535.32

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    Метою цього дослідження є вивчення кубічно-квартичних оптичних солітонів з використанням закону Кудряшова щодо самомодуляції фази. Для забезпечення неперервного існування солітонів в моделі передбачено комбінацію дисперсії третього (3OD) і четвертого (4OD) порядків. Дослідження проводиться за допомогою двох ефективних методів інтегрування, відомих як метод покращених проективних рівнянь Ріккаті та техніки анзацу солітона. Рішення солітонів, отримані на основі двох фізичних випадків, спрямованих на встановлення співідношення між 3OD і 4OD. У випадку, коли 3OD дорівнює чотирикратному значенню хвильового вектора 4OD, отримуються лише темні та сингулярні профілі солітонів. Однак, якщо це співвідношення не виконується,тоді генеруються різні структури солітонних імпульсів, включаючи кінк-темні, сингулярні, W-подібні, яскраві, темні, кінк та антикінк солітони. Фізичні інтерпретації отриманих оптичних солітонів представлені шляхом ілюстрації хвильової поведінки при певних значеннях параметрів моделі. Результати показують, що поєднання 3OD і 4OD має значний вплив на динаміку поширення солітонів.

    Ключові слова: оптичні солітони, кубічно-квартова дисперсія, закон Кудряшова, вдосконалений метод проективних рівнянь Ріккаті, солітонний анзац

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