At zero temperature, Bose-Einstein condensates (BEC) can be modeled by the famous

Gross-Pitaevskii equation (GPE) or coupled GPEs or nonlocal GPE.  In this talk,

the following three topics will be discussed:

(1) A review of different GPEs in modeling Bose-Einstein condensates at zero temperature.

(2) Numerical application of time-independent GPE into the study of ground state of BEC.

(3) Numerical application of time-dependent GPE into the investigation of dynamics of BEC.

Some open problems on ground state solution of BEC will be involved too.

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