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- Title
Vortex filament flows for curves in a 3-dimensional pseudo-Riemannian manifold.
- Authors
Yüzbai, Zühal Küçükarslan; Gürbüz, Nevin Ertug; Lee, Hyun Chul; Yoon, Dae Won
- Abstract
In this work, we focus on the evolution of the vortex filament flow ∂ γ ∂ t = ∂ γ ∂ s ∧ D ds ∂ γ ∂ 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 non-linear Schrödinger equation. Also, we give some examples to illustrate the vortex filament flow.
- Subjects
NONLINEAR Schrodinger equation; PARTIAL differential equations; FIBERS; HEAT equation; RIEMANNIAN manifolds
- Publication
Aequationes Mathematicae, 2024, Vol 98, Issue 1, p261
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-023-01030-4