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

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

In this paper, the parallel transport frames over non-lightlike curves in Minkowski 3-space are introduced. Evolution equations of these frames with respect to arc length and time are calculated over the space of these curves. Then the equivalence of the non-linear Schr\"odinger equation and no...

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Veröffentlicht in:arXiv.org 2013-10
Hauptverfasser: Gürbüz, Nevin, Cengiz, Süleyman
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Sprache:eng
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Curves
Evolution
Frames
Mathematical analysis
Minkowski space
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description In this paper, the parallel transport frames over non-lightlike curves in Minkowski 3-space are introduced. Evolution equations of these frames with respect 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-linear heat system to the vortex filament equation for the binormal motion of non-lightlike curves is shown by use of the parallel frames and their evolution equations.
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subjects Curves
Evolution
Frames
Mathematical analysis
Minkowski space
title Vortex Filament Equation and Non-Lightlike Space Curves in Minkowski 3-space
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