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

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    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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