Semiconductor Physics, Quantum Electronics & Optoelectronics, 29 (2), P. 203-210 (2026).
DOI: https://doi.org/10.15407/spqeo29.02.203


Cubic-quartic optical soliton perturbation with Fokas–Lenells equation having Kerr law of self-phase modulation by Laplace–Adomian decomposition

O. González-Gaxiola1, A. Biswas2,3,4,5,6*, Y. Yildirim7,8,9, C.D. Bălănică10, J.R. de Chávez11

1Applied Mathematics and Systems Department, Universidad Autónoma Metropolitana-Cuajimalpa, Vasco de Quiroga 4871, 05348 Mexico City, Mexico
2Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245–2715, USA
3Department of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon-61080, Türkiye
4Department of Physics and Electronics, Khazar University, Baku, AZ–1096, Azerbaijan
5Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa–0204, Pretoria, South Africa
6Applied Science Research Center, Applied Science Private University, Amman-11937, Jordan
7Department of Computer Engineering, Biruni University, Istanbul–34010, Turkey
8Mathematics Research Center, Near East University, 99138 Nicosia, Cyprus
9Faculty of Arts and Sciences, University of Kyrenia, 99320 Kyrenia, Cyprus
10Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati-800201, Romania
11Department of Mathematics, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, 09340, Mexico City, Mexico
*Corresponding author e-mail: biswas.anjan@gmail.com

Abstract. This paper addresses the perturbed Fokas–Lenells equation with a cubic-quartic form of dispersive effects and the Kerr law of self-phase modulation structures. The chromatic dispersive effect is replaced with a collective count of third- and fourth-order dispersions when the count on CD runs low. The Laplace–Adomian decomposition scheme made this numerical study possible. Both bright and dark optical solitons are studied using this principle. The error count is impressively low, thus making this numerical approach a viable one.

Keywords: Fokas–Lenells equation, Laplace–Adomian decomposition, cubic-quartic optical solitons.

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