Investigation of Bose–Einstein Condensation Dynamics by Homotopy Perturbation and Bernoulli Sub‐Equation Function Methods

ABSTRACT In this study, the dynamics of a quasi 1D Bose–Einstein condensate is investigated with the help of homotopy perturbation and Bernoulli sub‐equation function methods, and their effectiveness is compared. The quasi‐1D condensate, composed of interacting atoms at low temperatures and low densities, is modeled by the 1D Gross–Pitaevskii equation, which provides highly accurate results under the assumptions of mean‐field theory. In this context, the equation is considered both in the absence of a trap potential and in the presence of the Pöschl–Teller trap potential, which holds special significance in quantum mechanics. For the first time, the analysis of the 1D Gross–Pitaevski equation with the Pöschl–Teller trap potential is carried out using the Bernoulli sub‐equation function and homotopy perturbation methods.