Vortex filament flows for curves in a 3-dimensional pseudo-Riemannian manifold
Aequationes Mathematicae, cilt.98, sa.1, ss.261-274, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 98 Sayı: 1
- Basım Tarihi: 2024
- Doi Numarası: 10.1007/s00010-023-01030-4
- Dergi Adı: Aequationes Mathematicae
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
- Sayfa Sayıları: ss.261-274
- Anahtar Kelimeler: Evolution equation, Heat equation, Non-linear Schrödinger equation, Primary 53C50, Pseudo-Riemannian manifold, Secondary 35Q55, Vortex filament flow
- Eskişehir Osmangazi Üniversitesi Adresli: Evet
Özet
In this work, we focus on the evolution of the vortex filament flow ∂γ∂t=∂γ∂s∧Dds∂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.