Knotted configurations from the Gross-Pitaevskii equation

Abstract:
One of the most important features of realistic field theories, both in elementary particle theory and in applications to condensed matter systems, is their nonlinearity. The discovery of Bose-Einstein condensation in alkali gases is one of the most important results of physics in XX century. It is understood now that all the low temperature properties of Bose-Einstein condensation are well described by the Gross-Pitaevskii equation. As well-known the Gross-Pitaevskii equation is nonlinear and only for special classes of potentials certain exact solutions have been found (see, for example, [1]). The aim of this communication is to discuss possibilities to construct a knotted configurations related with the Gross-Pitaevskii equation. The results reported are based on article [2].

1. Enolskii V.Z. Towards algebra-geometric integration of the Gross-Pitaevskii equation. Nonlinear waves: Classical and Quantum Aspects. Eds. F.Kh.Abdullaev and V.V.Konotop. NATO Science Series. V.153. 3-14. 2004. Kluwer Academic Publishers.
2. Myrzakulov R. et al. Magnetic knots and links. Vestnik al-Farabi KazNU.