Hidden symmetry and knot solitons in a charged two-condensate Bose system

Abstract

We show that a charged two-condensate Ginzburg-Landau model or equivalently a Gross-Pitaevskii functional for two charged Bose condensates, can be mapped onto a version of the nonlinear O(3) \ensuremath{\sigma} model. This implies in particular that such a system possesses a hidden O(3) symmetry and allows for the formation of stable knotted solitons.