Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the Gross--Pitaevskii Equation
- 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
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
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE; US Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF)
- Grant/Contract Number:
- AC52-06NA25396; RGPIN-33798; RGPAS/461907; FA950-12-1-0332
- OSTI ID:
- 1394965
- Report Number(s):
- LA-UR-15-25770
- Journal Information:
- SIAM Journal on Applied Dynamical Systems, Vol. 15, Issue 2; ISSN 1536-0040
- Publisher:
- Society for Industrial and Applied MathematicsCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
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