  We generalize the Lund-Regge model for vortex string dynamics in
4-dimensional Minkowski space to the arbitrary n-dimensional case. The
n-dimensional vortex equation is identified with a nonabelian sine-Gordon
equation and its integrability is proven by finding the associated linear
equations of the inverse scattering. An explicit expression of vortex
coordinates in terms of the variables of the nonabelian sine-Gordon system is
derived. In particular, we obtain the n-dimensional vortex soliton solution of
the Hasimoto-type from the one soliton solution of the nonabelian sine-Gordon
equation.
