Discovering new abundant optical solutions for the resonant nonlinear Schrödinger equation using an analytical technique

In our exploration of optical physics, the intricate resonant nonlinear Schrödinger (NLS) equation featuring dual-power law nonlinearity is investigated which is an equation of paramount importance in the field of optics. This equation serves as a key to unlocking the intricacies of optical phenomena, including solitons, nonlinear effects, and wave interactions. Various optical solutions covering a broad variety of mathematical expressions, from trigonometric and hyperbolic functions to rational ones, are revealed by applying the technique of the powerful ( \(\dot{G}/G\) $\dot{G}/G$ , \(1/G\) $1/G$ )-expansion analytical approach which is the main goal of this study. The utmost precision and reliability of our findings are rigorously confirmed via the robust Mathematica software. Furthermore, the dynamic visual representations including 2D, 3D, and contour charts are presented to vividly depict various optical patterns such as single periodic, multi-periodic, singular soliton, and semi-bell-shaped phenomena. These solutions are of the utmost significance in the fields of nonlinear fiber optics and telecommunications, contributing to our comprehension of the fundamental physical concepts underlying the equation. The adaptability and application of our new and standardized technique is demonstrated by applying it to a wide range of mathematical and physical challenges.