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We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetictrap, modeled by an anisotropic harmonic potential. We evaluate the wavefunction and the energy of the Bose Einstein condensate as a function of theparticle number, both for positive and negative scattering length. The resultsfor the transverse and vertical size of the cloud of atoms, as well as for thekinetic and potential energy per particle, are compared with the predictions ofapproximated models. We also compare the aspect ratio of the velocitydistribution with first experimental estimates available for $^{87}$Rb. Vortexstates are considered and the critical angular velocity for production ofvortices is calculated. We show that the presence of vortices significantlyincreases the stability of the condensate in the case of attractiveinteractions.

Bosons in anisotropic traps: Ground state and vortices