Accurate perceptions of the bright and dark soliton solutions to the modified nonlinear Schrödinger equation

Abstract

In this study, we will implement new perceptions for the bright and dark soliton solutions to the modified nonlinear Schrödinger equation (MNLSE)or forms of the rogue wave modes for a derivative nonlinear Schrodinger model with positive linear dispersion which describe the propagation of rogue waves in Ocean engineering as well as all similar waves such as dynamics waveguides that have unexpected large displacements, the waves which occur only in the regime of positive cubic nonlinearity, regime that coincides exactly with the existence of instabilities of plane waves , long-wave limit of a breather (a pulsing mode). Two famous different schemas are involved for this purpose. The first schema is the solitary wave ansatze method (SWAM), while the second scheme is the extended simple equation method (ESEM). The two schemas are implemented in the same vein and parallel to construct new perceptions to the soliton solutions of this model. A comparison between the obtained new perceptions with the old perceptions that achieved previously by other authors has been demonstrated.