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In this paper, the parallel transport frames over non-lightlike curves inMinkowski 3-space are introduced. Evolution equations of these frames withrespect to arc length and time are calculated over the space of these curves.Then the equivalence of the non-linear Schr\"odinger equation and non-linearheat system to the vortex filament equation for the binormal motion ofnon-lightlike curves is shown by use of the parallel frames and their evolutionequations.

Vortex Filament Equation and Non-Lightlike Space Curves in Minkowski 3-space