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.