Modulational instability of the trapped Bose-Einstein condensates

Modulational instability in a trapped BEC is investigated both analytically and numerically. A new explicit time-dependent criteria for modulational instability of the trapped BEC is obtained. It is shown that a modulational unstable time scale exists. The modulational properties are modified significantly by the external trapping. The theoretical results are verified by the numerical integration of the fully Gross-Pitaevskii equation.