The Gross–Pitaevskii Equation (GPE) is a nonlinear partial differential equation that describes the behavior of Bose-Einstein condensates, which are states of matter formed at very low temperatures. It models the wave function of a condensate, capturing the interactions between particles and their collective behavior. The equation incorporates both the kinetic energy of particles and their potential energy due to interactions. It is essential in understanding phenomena such as superfluidity and quantum vortices in ultracold gases, providing insights into the macroscopic quantum effects that arise in these systems.