<p>This study extends the class of highly nonlinear Schrödinger equations by incorporating the resonant and cubic derivative terms, alongside infusing the quadrupled power-law nonlinearity term. This inclusion of terms is introduced in the present study, in addition to the proposal of an optimal analysis methodology. The modified Kudryashov method is employed for solitonic analysis. Further, the study constructs various sorts of exponential-logarithmic solutions that recast to singular and dark solitonic expressions, in addition to the construction of dissimilar supplementary optical solitons that pave the way for parametric analysis for optimal optical transmission of waves in a nonlinear medium. Remarkably, the reported graphical illustrations, which serve as the basis for the parametric analysis, indicated that the inclusion of the resonant term in the model proliferates the wave dynamics in the medium. At the same time, the incorporation of the cubic derivative term must vanish for the integrability condition to hold. Moreover, various effects have been noted by both the model’s and method’s parameters, besides the provision of the solitons’ stability and modulation instability analyses. In the end, the study recommends further study in the realm of highly nonlinear complex-valued evolution equations with emphasis on the contemporary fields of relevance, like optical communication, quantum field theory, and the design and analysis of fluid and waveguide structures, among others.</p>