Static solitary waves in axisymmetric Bose-Einstein condensates

S. Komineas^a and N. Papanicolaou^b
^aTheory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
^bDepartment of Physics, University of Crete, and Research Center of Crete, Heraklion, Greece

Abstract
Quasi-one-dimensional solitons that may occur in a confined axisymmetric Bose-Einstein condensate become unstable at high particle number. Here, we study two basic modes of instability and the corresponding bifurcations to axisymmetric vortex rings and non-axisymmetric solitonic vortices whose static profiles are calculated explicitly.