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Abstract
We study certain stationary and time-evolution problems oftrapped Bose-Einstein condensates using the numerical solutionof the Gross-Pitaevskii (GP) equation with both spherical and axialsymmetries. We consider time-evolution problems initiated by suddenlychanging the interatomic scattering length or harmonic trappingpotential in a stationary condensate. These changesintroduce oscillations in the condensate which are studied indetail. We use a time iterative split-step method for thesolution of the time-dependent GP equation, whereall nonlinear and linear non-derivative terms are treatedseparately from the time propagation with the kinetic energyterms. Even for an arbitrarily strong nonlinear term this leadsto extremely accurate and stable results after millions of timeiterations of the original equation.
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