Cubic-quartic optical soliton perturbation Biswas-Milovic equation with Kudryashov’s law of refractive index using two integration methods

Abstract In this paper, we introduce the cubic-quartic perturbation with Biswas-Milovic equation including Kudryashov’s law of refractive index. Two mathematical approaches, namely, the modified Kudryashov’s approach and the addendum to Kudryashov’s approach are used to obtain optical soliton solutions to this equation. Dark soliton, bright soliton and singular soliton solutions have been existed. The comparative analysis of the two proposed approaches shows that the first approach gives the dark and singular solitons while the second approach gives the bright and singular solitons.