Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the GrossPitaevskii Equation
For a dissipative variant of the twodimensional GrossPitaevskii 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 vortexfree 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 onedimensional 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
 Authors:

^{[1]};
^{[2]};
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^{[3]}
 Dalhousie Univ., Halifax (Canada). Dept. of Mathematics and Statistics
 Univ. of Massachusetts, Amherst, MA (United States). Dept. of Mathematics and Statistics
 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):
 LAUR1525770
Journal ID: ISSN 15360040
 Grant/Contract Number:
 AC5206NA25396; RGPIN33798; RGPAS/461907; FA9501210332
 Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Applied Dynamical Systems
 Additional Journal Information:
 Journal Volume: 15; Journal Issue: 2; Journal ID: ISSN 15360040
 Publisher:
 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
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Atomic and Nuclear Physics; Mathematics; nonlinear Schrodinger equation; BoseEinstein condensates; vortex nucleation; dissipative GrossPitaevskii equation
 OSTI Identifier:
 1394965
Tzou, J. C., Kevrekidis, P. G., Kolokolnikov, T., and CarreteroGonzález, R.. Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the GrossPitaevskii Equation. United States: N. p.,
Web. doi:10.1137/15M1038931.
Tzou, J. C., Kevrekidis, P. G., Kolokolnikov, T., & CarreteroGonzález, R.. Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the GrossPitaevskii Equation. United States. doi:10.1137/15M1038931.
Tzou, J. C., Kevrekidis, P. G., Kolokolnikov, T., and CarreteroGonzález, R.. 2016.
"Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the GrossPitaevskii Equation". United States.
doi:10.1137/15M1038931. https://www.osti.gov/servlets/purl/1394965.
@article{osti_1394965,
title = {Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the GrossPitaevskii Equation},
author = {Tzou, J. C. and Kevrekidis, P. G. and Kolokolnikov, T. and CarreteroGonzález, R.},
abstractNote = {For a dissipative variant of the twodimensional GrossPitaevskii 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 vortexfree 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 onedimensional 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},
doi = {10.1137/15M1038931},
journal = {SIAM Journal on Applied Dynamical Systems},
number = 2,
volume = 15,
place = {United States},
year = {2016},
month = {5}
}