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On the Gross–Pitaevskii equation for trapped dipolar quantum gases

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Published 29 September 2008 • 2008 IOP Publishing Ltd and London Mathematical Society
, , Citation Rémi Carles et al 2008 Nonlinearity 21 2569 DOI 10.1088/0951-7715/21/11/006

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1 CNRS and University Montpellier 2, Mathématiques, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France

2 Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, UK

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  1. Received 5 May 2008
  2. Published

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0951-7715/21/11/2569

Abstract

We study the time-dependent Gross–Pitaevskii equation describing Bose–Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension reduction for this nonlinear and nonlocal Schrödinger equation.

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10.1088/0951-7715/21/11/006