Abstract: Symplectic method is applied to solve numerically 1D time-dependent Gross-Pitaevskii equation. "Breathing" of the condensate is numerically illustrated. Interaction of two Bose-Einstein condensates is investigated as external potential is zero at t=0. Interference between two condensates is observed. Evolution of density due to interference at various relative phases is studied.

Key words: Gross-Pitaevskii equation, ODA method, symplectic method, phase difference