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We derive the governing equations of vortices for the nonlinear wave
equation. The initial data is a small perturbation of the symmetric vortex solution
in the steady state Ginzburg-Landau equation. Then by the well-posedness of the
nonlinear wave equation (cf. ) and the spectrum of the linearized operator for
the Ginzburg-Landau equation (cf. , ), we obtain the local dynamic laws of
vortices in a short time.