Using variational and perturbative methods we investigate the dynamics of a trapped Bose-Einstein condensate whose effective nonlinearity is harmonically modulated. We derive analytic formulae for the period of Faraday waves in lowand high-density, longitudinally-homogeneous condensates. Using the Poincaré- Lindstedt analysis, we also analytically calculate frequency shifts of collective oscillation modes of spherically and axially-symmetric condensates due to the harmonic driving of the interaction.
Bose-Einstein condensates Faraday waves collective modes perturbation theory variational treatment
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