Weakly nonlinear analysis of vortex formation in a dissipative variant of the Gross-Pitaevskii equation

J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-Gonzalez

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)904–922
Number of pages19
JournalSIAM Journal on Applied Dynamical Systems
Volume15
Issue number2
DOIs
Publication statusPublished - 2016
Externally publishedYes

Keywords

  • nonlinear Schrödinger equation
  • Bose–Einstein condensates
  • vortex nucleation
  • dissipative Gross– Pitaevskii equation

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