G.N.Nugmanova, T.R.Myrzakul, R.Myrzakulov (Eurasian National University, Astana, Kazakhstan)

Knotted configurations from the Gross-Pitaevskii equation

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.