2009/08/08 by Renato Fedele, R. Fedele, Dusan Jovanovic +5
Mathematics · Physics and Astronomy · #Bose–Einstein condensate #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Gross–Pitaevskii equation #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Physics #Quantum mechanics #Stability (learning theory) #Strong Light-Matter Interactions #cond-mat.quant-gas
paper · pdf · doi:10.1140/epjb/e2010-00052-3
21 pages, 14 figures
arxiv created 2009/08/08 · openalex publication_date 2010/02/16 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs). The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schrödinger equation and a one-dimensional (1D) nonlinear Schrödinger equation, constrained by a variational condition for the controlling potential. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. On the basis of these exact 3D analytical solutions, a stability analysis is carried out, focusing our attention on the physical conditions for having collapsing or non-collapsing solutions.