Gross-pitaevskii equation is a fundamental theoretical model in condensed matter physics and ultracold atom research. It serves as a non-linear Schrödinger equation describing the wavefunction of a Bose-Einstein condensate (BEC) in the mean-field approximation. This concept is significant as it provides a powerful framework for investigating the macroscopic quantum phenomena, dynamics, and static properties of weakly interacting bosonic systems at extremely low temperatures, predicting crucial behaviors like superfluidity and vortex formation.