Vortices for the nonlinear wave equation (Q1576831)

Local dynamic laws for the short-time evolution of two-dimensional vortices governing by a nonlinear wave equation are derived in the paper. A small perturbation of the symmetric vortex solution of steady-state Ginzburg-Landau equation is used as initial data. A harmonic function is used as the leading term in the phase function of the far field expansion instead of that satisfying a linear wave equation. This leads to the absence of the memory effect in the dynamics of vortices and simplifies the governing equations of vortices.