Quasi-one-dimensional approximation for Bose–Einstein condensates transversely trapped by a funnel potential

  title={Quasi-one-dimensional approximation for Bose–Einstein condensates transversely trapped by a funnel potential},
  author={Mateus C. P. dos Santos and Boris A. Malomed and Wesley B. Cardoso},
  journal={Journal of Physics B: Atomic, Molecular and Optical Physics},
Starting from the standard three-dimensional (3D) Gross–Pitaevskii equation (GPE) and using a variational approximation, we derive an effective one-dimensional nonpolynomial Schrödinger equation (1D-NPSE) governing the axial dynamics of atomic Bose–Einstein condensates (BECs) under the action of a singular but physically relevant funnel-shaped transverse trap, i.e. an attractive 2D potential ∼−1/r (where r is the radial coordinate in the transverse plane), in combination with the repulsive self… 
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