Two infinite families of resonant solutions for the Gross-Pitaevskii equation

Anxo Biasi, Piotr Bizoń, Ben Craps, and Oleg Evnin
Phys. Rev. E 98, 032222 – Published 26 September 2018

Abstract

We consider the two-dimensional Gross-Pitaevskii equation describing a Bose-Einstein 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 angular-momentum 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.

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  • Received 10 May 2018

DOI:https://doi.org/10.1103/PhysRevE.98.032222

©2018 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

Anxo Biasi1, Piotr Bizoń2, Ben Craps3, and Oleg Evnin4,3

  • 1Departamento de Física de Partículas, Universidade de Santiago de Compostela and Instituto Galego de Física de Altas Enerxías (IGFAE), Santiago de Compostela 15782, Spain
  • 2Institute of Physics, Jagiellonian University, Kraków 30-348, Poland
  • 3Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB) and The International Solvay Institutes, B-1050 Brussels, Belgium
  • 4Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand

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Issue

Vol. 98, Iss. 3 — September 2018

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