The dynamics of vortex lines in the three-dimensional complex Ginzburg-Landau equation: instability, stretching, entanglement, and helices

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Abstract
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 shown that a straight vortex line is unstable with respect to spontaneous stretching and bending in a substantial range of parameters of the CGLE, resulting in formation of persistent entangled vortex configurations. The boundary of the three-dimensional instability in parameter space is determined. Near the stability boundary, the supercritical saturation of the instability is found, resulting in the formation of stable helicoidal vortices.

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