New unexpected soliton solutions to the generalized (2 + 1) Schrödinger equation with its four-mixing waves

Abstract

The propagation of solitons in birefringent fiber is one of the phenomena that has an important role in all modern technological means of communication. The generalized [Formula: see text] nonlinear Schrödinger equation (GNLSE) with its four-mixing waves (FMW) is the famous model that describes the propagation of solitons in birefringent fiber perfectly. In fact, the FMW governed effectively the performance of the resultant solitons amplitude. Hereby, we will study this model to extract new unexpected optical soliton solutions to this model via various three techniques. The three famous methods that are a candidate for this purpose are the extended direct algebraic method (EDAM), the extended simple equation method (ESEM) and the solitary wave ansatz method (SWAM). The three techniques are implemented successively for the suggested model to establish the optical solutions of the suggested model successfully. The optical soliton solutions that are achieved by these proposed techniques give surprise expectations that weren’t achieved previously by any other authors who used other techniques.