Ukrainian Journal of Physical Optics


2022 Volume 23, Issue 4


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

Cubic-quartic optical solitons for Lakshmanan-Porsezian-Daniel equation by the improved Adomian decomposition scheme

A. A. Al Qarni, A. M. Bodaqah, A. S. H. F. Mohammed, A. A. Alshaery, H. O. Bakodah and A. Biswas

Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Saudi Arabia, aqarny@ub.edu.sa
Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah, Saudi Arabia.
Department of Mathematics and Physics, Grambling State University, Grambling, LA-71245, USA.
Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah-21589, Saudi Arabia.
Department of Applied Sciences, Cross-Border Faculty, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati-800201, Romania.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, South Africa.

ABSTRACT

We study a class of Lakshmanan–Porsezian–Daniel equations endowed with a cubic–quartic nonlinearity. A highly efficient improved Adomian decomposition approach is employed when deriving a generalized numerical scheme. Our numerical results reveal perfect agreement with the analytical optical solutions known from the literature. In other words, our method provides an astonishing level of accuracy and reliability.

Keywords: optical solitons, Lakshmanan-Porsezian-Daniel model, Kerr-law nonlinearity, improved Adomian decomposition method

UDC: 535.32

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    Досліджено клас рівнянь Лакшманана–Порсезіана–Даніеля, наділених кубічно-квартичною нелінійністю. В отриманні узагальненої числового підходу використано високоефективну покращену схему розкладання Адоміана. Наші чисельні результати виявляють ідеальну згоду з аналітичними рішеннями для оптики, відомими з літератури. Іншими словами, наш метод забезпечує вражаючий рівень точності та надійності.

    Ключові слова: оптичні солітони, модель Лакшманана–Порсезіана–Даніеля, керрівська нелінійність, покращений метод розкладання Адоміана

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