In this study, we examine the dynamic behavior of optical solitons in the nonlinear conformable Gross–Pitaevskii equation (GPE) within Bose–Einstein condensates, which refer to the phenomenon of many ultra-cold bosonic particles occupying a single quantum state. The GPE is a cornerstone of advanced statistical physics, has application in various engineering disciplines, particularly in the realm of quantum mechanics and optical engineering. By precisely encoding the GPE’s steady-state solutions, we make it possible to compute nonlinear models pertinent to engineering systems and clarify solutions within particular parameter regimes that are essential for engineering applications. Our study encompasses repulsive and attractive nonlinearities in GPE, including quadratic and double-well potentials. We focus on discovering solutions, employing the generalized Riccati equation mapping method and modified extended tanh-function method to extract soliton solutions. The study yields a variety of soliton including combined dark–bright, singular, combo dark-singular, periodic-singular, and rational solutions with physical perspectives. Through 2D and 3D representations, the internal structure of these phenomena is effectively illustrated, offering insights into their behavior and dynamics, which is significant for optimization process and engineering design.
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