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Dynamics of vortex dipoles in confined Bose–Einstein condensates

2011; Elsevier BV; Volume: 375; Issue: 33 Linguagem: Inglês

10.1016/j.physleta.2011.06.061

1873-2429

Pedro J. Torres, P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, Peter Schmelcher, D. S. Hall,

Strong Light-Matter Interactions

We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose–Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.