Publication Date
2015
Abstract
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. 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.
Pages
17
Recommended Citation
Tzou, J. C.; Kevrekidis, P. G.; Kolokolnikov, T.; and Carretero-González, R., "Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the Gross-Pitaevskii Equation" (2015). Mathematics and Statistics Department Faculty Publication Series. 1239.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1239