In this article, we will study the modified nonlinear Schr¨odinger equation which represents the
propagation of rogue waves in ocean engineering that occur in deep water, usually far out at sea,
and are a threat even to capital ships and ocean liners. In related subject for all like waves which
occurred at different branches of science which have the same behaviors such as fluid dynamics
waveguides that have unexpected large displacements, long-wave limit of a breather (a pulsing
mode), telecommunications engineering devices, etc. We will implement new multiple visions for
the soliton solution to the modified nonlinear Schr¨odinger equation (MNLSE) that describes
successfully these phenomenon. Studying this important model and its own behavior of the
resulting solitons description will contribute effectively in marine safety and improvement the
pulse devices which cooperate to protect human life effectively and technology for high-capacity
optical communications through which the modern asocial media was built…etc. Three different
techniques are invited for this purpose. The first technique is the Paul-Painlev´e approach method
(PPAM), while the second technique is the Ricatti-Bernolli Sub ODE method (RBSOM). In related
subject, the variational iteration method VIM is implemented in the same vein and parallel to
construct the numerical solutions corresponding to the achieved soliton solutions via each one of
these two methods individually. A good comparison not only between these three visions of
soliton solutions but also with that achieved previously by other authors has been demonstrated. |
