Dynamical Behavior Of Double Quantum Vortices

Quantized vortex is a kind of wave with phase singularity and rotating flow around singularities,which results from the special topological structure caused by the symmetry breaking of the gauge field model.Quantized vortices have been widely used in superconductors,superfluids,condensed matter and so on.The nonlinear wave equation can well describe the dynamic behavior of quantized vortices.In this paper,we consider nonlinear wave equation under the reduced dy-namic law?where z_j=?x_j,y_j?T ? R² is the center of the j-th vortex,mj is the mass of the j-th vortex,N is the number of quantized vortices.The main purpose of this paper is to study the interaction of quantized vortices in a reduced dynamical system at N=2.With the help of phase plane analysis,a complete description of the dynamic behavior of dipole?m₁=-m₂= 1?and vortex pairs?m₁=m₂=1?is given.