D.E. Pelinovsky and P.G. Kevrekidis

Variational approximations of trapped vortices in the large-density limit

Nonlinearity 24 (2011), 1271-1289

The Gross–Pitaevskii equation with a harmonic potential and repulsive nonlinear interactions is considered in the large-density limit, also known as the Thomas–Fermi limit. In the space of two dimensions, we employ the Rayleigh–Ritz approximation method to obtain variational approximations of single vortices, dipole pairs, and quadrupoles trapped in the harmonic potential. In particular, we compute the eigenfrequency of the single vortex precession about the center of symmetry of the harmonic potential, as well as the eigenfrequencies of the oscillations of the dipole and quadrupole vortex configurations. The asymptotic results are confirmed by the numerical computations of the vortex states and the linearization thereof.

Gross-Pitaevskii equation, harmonic potential, Thomas-Fermi limit, semi-classical limit, variational Rayleigh-Ritz method, vortex configurations