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

被引：0

作者：

Yuzbai, Zuhal Kucukarslan ^{[1
]}

Gurbuz, Nevin Ertug ^{[2
]}

Lee, Hyun Chul ^{[3
,4
]}

Yoon, Dae Won ^{[3
,4
]}

机构：

[1] Fırat Univ, Dept Math, TR-23119 Elazig, Turkiye

[2] Eskisehir Osmangazi Univ, Dept Math & Comp Sci, Eskisehir, Turkiye

[3] Gyeongsang Natl Univ, Dept Math Educ, Jinju 52828, South Korea

[4] Gyeongsang Natl Univ, RINS, Jinju 52828, South Korea

来源：

AEQUATIONES MATHEMATICAE | 2024年 / 98卷 / 01期

关键词：

Vortex filament flow; Non-linear Schrodinger equation; Heat equation; Evolution equation; Pseudo-Riemannian manifold; BINORMAL MOTION; SOLITON; EQUATIONS; TORSION;

D O I：

10.1007/s00010-023-01030-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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

引用

页码：261 / 274

页数：14

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