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

Yüzbai Z. K., GÜRBÜZ Ş. N., Lee H. C., Yoon D. W.

Aequationes Mathematicae, cilt.98, sa.1, ss.261-274, 2024 (SCI-Expanded) identifier identifier

  • 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.