Vortex filament flows for curves in a 3-dimensional pseudo-Riemannian manifold
- Authors
- Yuzbai, Zuhal Kucukarslan; Gurbuz, Nevin Ertug; Lee, Hyun Chul; Yoon, Dae Won
- Issue Date
- Feb-2024
- Publisher
- Birkhauser Verlag
- Keywords
- Vortex filament flow; Non-linear Schrodinger equation; Heat equation; Evolution equation; Pseudo-Riemannian manifold
- Citation
- Aequationes Mathematicae, v.98, no.1, pp 261 - 274
- Pages
- 14
- Indexed
- SCIE
SCOPUS
- Journal Title
- Aequationes Mathematicae
- Volume
- 98
- Number
- 1
- Start Page
- 261
- End Page
- 274
- 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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