On Bäcklund transformation and vortex filament equation for null Cartan curve in Minkowski 3-space
| Autor: | Emilija Nešović, Emilija Nesovic, Milica Grbović |
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| Rok vydání: | 2016 |
| Předmět: |
010102 general mathematics
Mathematical analysis Vortex filament 01 natural sciences 010305 fluids & plasmas General Relativity and Quantum Cosmology 0103 physical sciences Evolution equation Minkowski space Torsion (algebra) Mathematics::Differential Geometry Geometry and Topology 0101 mathematics Mathematics::Representation Theory Mathematical Physics Mathematics |
| Zdroj: | Mathematical Physics, Analysis and Geometry. 19 |
| ISSN: | 1572-9656 1385-0172 |
| DOI: | 10.1007/s11040-016-9231-z |
| Popis: | In this paper we introduce Backlund transformation of a null Cartan curve in Minkowski 3-space as a transformation which maps a null Cartan helix to another null Cartan helix, congruent to the given one. We also give the sufficient conditions for a transformation between two null Cartan curves in the Minkowski 3-space such that these curves have equal constant torsions. By using the Da Rios vortex filament equation, based on localized induction approximation, we derive the vortex filament equation for a null Cartan curve and obtain evolution equation for it’s torsion. As an application, we show that Cartan’s frame vectors generate new solutions of the Da Rios vortex filament equation. |
| Databáze: | OpenAIRE |
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