Application of guaranteeing analytical methods in the construction of optical structures for nonlinear Schrödinger equations

This study gives some insights into the dynamics of pulse propagation in optical mediums governed by the perturbed Gerdjikov–Ivanov and nonlinear resonant Schrödinger equations via some effective analytical methods. The applications of the enhanced Kudryashov method and the auxiliary equation method have been deployed to construct several bright, dark, singular and bright–dark combo solitons for the two models. Moreover, as the Kudryashov-based method gave less solution sets in the case of the nonlinear resonant Schrödinger equation, the study further necessitates the involvement of the efficient addendums to Kudryashov method to yet unravel more solitonic expressions. Certainly, all the methods worked effectively, with the addendum to Kudryashov method II revealing special solution sets for the nonlinear resonant Schrödinger equation when [Formula: see text] All-in-all, the study recaps by recommending a thorough examination into the evolution of waves in highly nonlinear complex-valued models; in addition to the suggestion of sophisticated methodologies for tackling assorted nonlinear Schrödinger equations. In the end, some graphical illustrations are supplied, shedding more light on the dynamics of optical waves in the governing nonlinear medium—featuring the significance of temporal, group-velocity dispersion, nonlinearity-order, and the logarithmic parameters on the evolution of waves in the nonlinear optical medium.