A nonlinear Schrödinger equation including the parabolic law and its dark solitons

The main goal of the current paper is to analyze nonlinear effects on dynamical feathers of soliton waves in a nonlinear Schrödinger equation (NLSE) including the parabolic law. To this end, after applying the complex envelope and distinguishing real and imaginary structures, a group of dark solitons to the governing model are retrieved using the Kudryashov method. Based on the results, by adjusting the values of nonlinear effects, the amplitude of the dark solitons can be easily controlled.