Construction optical solitons of generalized nonlinear Schro<spacing diaeresis>dinger equation with quintuple power-law nonlinearity using Exp-function, projective Riccati, and new generalized methods

This work investigates the generalized nonlinear Schro<spacing diaeresis>dinger equation (NLSE), which imitates the wave transmission along optical fibers. This model incorporates a quintuple power-law of non-linearity and nonlinear chromatic dispersion. To demonstrate the significance and motivation for this work, a review of the prior research is presented in the literature. Three integration strategies are applied during the study process in order to produce a variety of novel solutions. These techniques include the modified exp-function approach, the general projective Riccati method (GPRM), and the new generalized method. The extracted solutions include bright solitons, singular solitons, dark solitons, and trigonometric solutions.