Yang, SJ (reprint author), Beijing Normal Univ, Dept Phys, Beijing 100875, Peoples R China.
The knot of the spin-texture is studied within the two-component Bose-Einstein condensates which are described by the nonlinear Gross-Pitaevskii equations. We start from the noninteracting equations including an axisymmetric harmonic trap to obtain an exact solution, which exhibits a nontrivial topological structure. The spin-texture is a knot with an integral Hopf invariant. The stability of the knot is verified by numerically evolving the nonlinear Gross-Pitaevskii equations along imaginary time. Copyright (C) EPLA, 2014