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

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) $\sigma$-model. This implies in particular that such a system possesses a hidden O(3) symmetry and allows for the formation of stable knotted solitons. The results, in particular, should be relevant to the superconducting MgB_2.Comment: This version will appear in Phys. Rev. B, added a comment on the case when condensates in two bands do not independently conserve, also added a figure and references to experimental papers on MgB_2 (for which our study is relevant). Miscellaneous links on knot solitons are also available at the homepage of one of the authors http://www.teorfys.uu.se/PEOPLE/egor/ . Animations of knot solitons are available at http://users.utu.fi/h/hietarin/knots/c45_p2.mp