New exact solutions for perturbed nonlinear Schrödinger’s equation with self-phase modulation of Kudryashov's sextic power law refractive index

In this work, the perturbed nonlinear Schrödinger’s equation (NLSE) with self-phase modulation (SPM) of Kudryashov’s sextic power law which describes the soliton's propagation in optical fiber is investigated. New exact solutions will be introduced including doubly periodic solutions in the form of Weirstrass and hyperbolic functions by using the simple equation method. There have been several different kinds of optical soliton solutions proposed, including dark, bright, kink, and anti-kink soliton solutions. To further understand some of its physical characteristics, the resulting optical soliton solutions are illustrated graphically.