Abstract
In this paper, we introduce the fiber Bragg gratings for cubic-quartic perturbed Lakshmanan-Porsezian-Daniel equation with Kerr law nonlinearity. Two mathematical methods, namely, the modified Kudryashov's method and the addendum to Kudryashov's method are applied to obtain optical soliton solutions to this equation. Dark soliton, bright soliton and singular soliton solutions have been found. The comparative analysis of the two proposed methods shows that the first method gives the dark and singular solitons while the second method gives the bright and singular solitons.