Cubic-Quartic Optical Soliton Perturbation for Fokas-Lenells Equation by Laplace-Adomian Decomposition

Abstract The present paper focuses on the cubic-quartic optical solitons modeled by the Fokas-Lenells equation. The Hamiltonian perturbation terms that are examined in the paper are of maximal intensity, while the self-phase modulation is governed by Kerr’s law. The paper employs the Laplace-Adomian numerical scheme, which produces bright soliton solutions with remarkable precision. The error graphs are presented in conjunction with the surface and density plots of the solitons. The findings indicate that these solitons exhibit stable propagation characteristics under certain parameter conditions. Furthermore, we analyze their behavior in various nonlinear media, shedding light on potential applications in fiber optics and photonic devices.