Numerical solution to the time-dependent Gross-Pitaevskii equation - Tsednee, Tsogbayar; Tsednee, Banzragch; Khinayat, Tsookhuu (Journal of Applied Science and Engineering A, 2022)
In this work we employ the split-step technique combined with a Legendre pseudospectral representation to solve various time-dependent GrossPitaevskii equations (GPE). Our findings based on the numerical accuracy of this approach applied for one-dimensional (1D) and two-dimensional (2D) problems show that it can provide accurate and stable solutions. Moreover, this approach has been applied to study the dynamics of the Bose-Einstein condensate which is modeled with the GPE. The breathing of condensate with a repulsive and attractive interactions trapped in 1D and 2D harmonic potentials has been simulated as well.