  The dynamics of curved vortex filaments is studied analytically and
numerically in the framework of a three-dimensional complex Ginzburg-Landau
equation (CGLE). It is proved that a straight vortex line is unstable with
respect to spontaneous stretching and bending in a certain range of parameters
of the CGLE, resulting in formation of persistent entangled vortex
configurations. The analysis shows that the standard approach relating the
velocity of the filament with the local curvature, is insufficient to describe
the instability and self-generation of vorticity.

Pattern Formation and Solitons;Pattern Formation and Solitons