# American Institute of Mathematical Sciences

April  1999, 5(2): 391-398. doi: 10.3934/dcds.1999.5.391

## Vortices for the nonlinear wave equation

 1 Department of Mathematics, Chung-Cheng University, Taiwan

Received  January 1998 Revised  October 1998 Published  January 1999

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.
Citation: Tai-Chia Lin. Vortices for the nonlinear wave equation. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 391-398. doi: 10.3934/dcds.1999.5.391
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