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Vortices for the nonlinear wave equation

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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. [12]) and the spectrum of the linearized operator for the Ginzburg-Landau equation (cf. [9], [8]), we obtain the local dynamic laws of vortices in a short time.
    Mathematics Subject Classification: 35061.

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