- Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi
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- Geometric Analysis of the NLS Surface with the Pseodu Null Darboux Frame of Spacelike Curve
Geometric Analysis of the NLS Surface with the Pseodu Null Darboux Frame of Spacelike Curve
Authors : Melek Erdoğdu, Ayşe Yavuz
Pages : 188-198
Doi:10.47112/neufmbd.2024.42
View : 75 | Download : 77
Publication Date : 2024-04-30
Article Type : Research
Abstract :In this study, examination of the vortex filament equation, known as the smoke ring equation, is given by considering it as a dynamic system associated with a unit speed spacelike curve in Minkowski space. Using the Darboux framework, the differential geometric features of the soliton surface that relate to the nonlinear Schrödinger (NLS) equation were investigated. This surface is often called the NLS surface or Hasimoto surface. Additionally, Gaussian and the mean curvatures of the NLS surface were determined using the Darboux curvatures. By providing an in-depth look at the geometric properties of the NLS surface, this analysis will make a significant contribution to increasing knowledge in this field and shedding light on potential applications.Keywords : Darboux çatısı, Doğrusal olmayan Schrödinger denklemi, Hasimoto yüzeyi