Effective wave equations for the dynamics of cigar-shaped and disk-shaped Bose condensates

L. Salasnich, A. Parola, and L. Reatto
Phys. Rev. A 65, 043614 – Published 2 April 2002
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Abstract

Starting from the three-dimensional (3D) Gross-Pitaevskii equation and using a variational approach, we derive an effective 1D wave equation that describes the axial dynamics of a Bose condensate confined in an external potential with cylindrical symmetry. The trapping potential is harmonic in the transverse direction and generic in the axial one. Our equation, that is a time-dependent nonpolynomial nonlinear Schrödinger equation (1D NPSE), can be used to model cigar-shaped condensates, whose dynamics is essentially 1D. We show that 1D NPSE gives much more accurate results than all other effective equations recently proposed. By using 1D NPSE we find analytical solutions for bright and dark solitons, which generalize the ones known in the literature. We deduce also an effective 2D nonpolynomial Schrödinger equation (2D NPSE) that models disk-shaped Bose condensates confined in an external trap that is harmonic along the axial direction and generic in the transverse direction. In the limiting cases of weak and strong interaction, our approach gives rise to Schrödinger-like equations with different polynomial nonlinearities.

  • Received 1 June 2001

DOI:https://doi.org/10.1103/PhysRevA.65.043614

©2002 American Physical Society

Authors & Affiliations

L. Salasnich1, A. Parola2, and L. Reatto1

  • 1Istituto Nazionale per la Fisica della Materia, Unità di Milano Università, Dipartimento di Fisica, Università di Milano, Via Celoria 16, 20133 Milano, Italy
  • 2Istituto Nazionale per la Fisica della Materia, Unità di Como, Dipartimento di Scienze Fisiche, Università dell’Insubria, Via Valleggio 11, 23100 Como, Italy

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Issue

Vol. 65, Iss. 4 — April 2002

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