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Vortex filament flows for curves in a 3-dimensional pseudo-Riemannian manifold

Authors
Yuzbai, Zuhal KucukarslanGurbuz, Nevin ErtugLee, Hyun ChulYoon, Dae Won
Issue Date
Jan-2024
Publisher
SPRINGER BASEL AG
Keywords
Vortex filament flow; Non-linear Schrodinger equation; Heat equation; Evolution equation; Pseudo-Riemannian manifold
Citation
AEQUATIONES MATHEMATICAE
Indexed
SCIE
SCOPUS
Journal Title
AEQUATIONES MATHEMATICAE
URI
https://scholarworks.gnu.ac.kr/handle/sw.gnu/69703
DOI
10.1007/s00010-023-01030-4
ISSN
0001-9054
1420-8903
Abstract
In this work, we focus on the evolution of the vortex filament flow partial derivative gamma|partial derivative iota = partial derivative gamma|partial derivative s boolean AND D|ds partial derivative gamma|partial derivative s for spacelike and timelike curves in a 3-dimensional pseudo-Riemannian manifold. We study the relations between a partial differential equation and the vortex filament flow for spacelike and timelike curves. As a result, we prove that the vortex filament flow of the spacelike curve in a 3-dimensional pseudo-Riemannian manifold with constant sectional curvature is equivalent to the heat equation, and the flow of the timelike curve is equivalent to the nonlinear Schr<spacing diaeresis>odinger equation. Also, we give some examples to illustrate the vortex filament
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