Vortex dynamics for the nonlinear wave equation

Vortex dynamics for the nonlinear wave equation is a typical model of the “particle and field” theories of classical physics. The formal derivation of the dynamical law was done by J.Neu. He also made an interesting connection between vortex dynamics and the Dirac theory of electrons. Here we give a rigorous mathematical proof of this natural dynamical law. © 1999 John Wiley & Sons, Inc.