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Abstract
We consider the twodimensional GrossPitaevskii equation describing a BoseEinstein condensate in an isotropic harmonic trap. In the small coupling regime, this equation is accurately approximated over long times by the corresponding nonlinear resonant system whose structure is determined by the fully resonant spectrum of the linearized problem. We focus on two types of consistent truncations of this resonant system: first, to sets of modes of fixed angular momentum, and, second, to excited Landau levels. Each of these truncations admits a set of explicit analytic solutions with initial conditions parametrized by three complex numbers. Viewed in position space, the fixed angularmomentum solutions describe modulated oscillations of dark rings, while the excited Landau level solutions describe modulated precession of small arrays of vortices and antivortices. We place our findings in the context of similar results for other spatially confined nonlinear Hamiltonian systems in recent literature.
Original language  English 

Article number  032222 
Number of pages  12 
Journal  Physical Review E 
Volume  98 
Issue number  3 
DOIs  
Publication status  Published  26 Sep 2018 
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 1 Active

SRP8: Strategic Research Programme: HighEnergy Physics at the VUB
D'Hondt, J., Van Eijndhoven, N., Craps, B. & Buitink, S.
1/11/12 → 31/10/22
Project: Fundamental