In this work, we construct suitable generating functions for vortices of alternating signs in the realm of Bose-Einstein condensates. In addition to the vortex-vortex interaction included in earlier fluid dynamics constructions of such functions, the vortices here precess around the center of the trap. This results in the generating functions of the vortices of positive charge and of negative charge satisfying a modified, so-called, Tkachenko differential equation. From that equation, we...
Topics: Nonlinear Sciences, Quantum Gases, Mathematics, Pattern Formation and Solitons, Mathematical...
Source: http://arxiv.org/abs/1407.7965
