中文摘要：

We investigate a kind of solitons in the two-component Bose–Einstein condensates with axisymmetric configurations in the R2×S1space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional(3D) skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross–Pitaevskii equations in imaginary time.

英文摘要：

We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R2 × S1 space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional （3D） skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time.