Vortex structure of Gross–Pitaevskii model

The vortex line of the Gross–Pitaevskii model is studied. The kinetic helicity of the vortex is discussed, and vortex structure is classified by the Hopf index, linking number in geometry. A mechanism of generation and annihilation of vortex lines is given by the method of phase singularity theory. The dynamic behavior of the vortex at the critical points is discussed in detail, and three kinds of length approximation relations at the neighborhood of a critical point are given: l ∝ (t − t∗)1/2, l ∝ t − t∗, l = const.