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Title: Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the Gross--Pitaevskii Equation

For a dissipative variant of the two-dimensional Gross--Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas$-$Fermi radius. The instability occurs as a result of a linear instability of a vortex-free steady state as the rotation is increased above a critical threshold. We focus on the second subsequent symmetry breaking, which occurs in the weakly nonlinear regime. At slightly above threshold, we derive a one-dimensional amplitude equation that describes the slow evolution of the envelope of the initial instability. Here, we show that the mechanism responsible for initiating vortex formation is a modulational instability of the amplitude equation. We also illustrate the role of dissipation in the symmetry breaking process. All analyses are confirmed by detailed numerical computations
 [1] ;  [2] ;  [1] ;  [3]
  1. Dalhousie Univ., Halifax (Canada). Dept. of Mathematics and Statistics
  2. Univ. of Massachusetts, Amherst, MA (United States). Dept. of Mathematics and Statistics
  3. San Diego State Univ., San Diego, CA (United States). Nonlinear Dynamical System Group Computational Science Research Center, and Dept. of Mathematics and Statistics
Publication Date:
Report Number(s):
Journal ID: ISSN 1536-0040
Grant/Contract Number:
AC52-06NA25396; RGPIN-33798; RGPAS/461907; FA950-12-1-0332
Accepted Manuscript
Journal Name:
SIAM Journal on Applied Dynamical Systems
Additional Journal Information:
Journal Volume: 15; Journal Issue: 2; Journal ID: ISSN 1536-0040
Society for Industrial and Applied Mathematics
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE; US Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; Atomic and Nuclear Physics; Mathematics; nonlinear Schrodinger equation; Bose-Einstein condensates; vortex nucleation; dissipative Gross-Pitaevskii equation
OSTI Identifier: