Adiabaticity in nonlinear quantum dynamics: Bose-Einstein condensate in a time-varying box

A simple model of an atomic Bose-Einstein condensate in a box whose size varies with time is studied to determine the nature of adiabaticity in the nonlinear dynamics obtained within the Gross-Pitaevskii equation (the nonlinear Schr\"odinger equation). Analytical and numerical methods are used to determine the nature of adiabaticity in this nonlinear quantum system. Criteria for validity of an adiabatic approximation are formulated.