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Vortex dynamics for the nonlinear wave equation. (English) Zbl 0929.35076
The author discusses three canonical nonlinear partial differential equations in the dynamics of the Ginzburg-Landau vortices with space dimension two. He gives a rigorous mathematical proof of the dynamical law, which describes the connection between vortex dynamics and the Dirac theory of electrons.

35L20 Initial-boundary value problems for second-order hyperbolic equations
35L70 Second-order nonlinear hyperbolic equations
Full Text: DOI
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