New expectations to soliton arising from the (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with four waves mixing via three different techniques

From the point of view of three famous and important techniques we will achieve new expectations for the soliton configurations to the (2+1)-dimensional generalized nonlinear Schrödinger equation (GNLSE) with four waves mixing (FWM). The suggested model describes propagation of solitons in birefringent fiber. The FWM governed effectively the performance of the resultant soliton amplitudes. The three famous methods candidates 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 successfully. Surprise expectations for solitons via these three techniques to this model which weren’t achieved previously by any other authors who used other techniques have been demonstrated.