2024/05/20 by Ahmet Kazan, Kazan, Ahmet, Mustafa Altın +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2406.05139
openalex publication_date 2024/05/20 · openalex created_date 2024/06/12 · openalex updated_date 2026/07/28
In this paper, for a soliton surface Ω=Ω(u,v) associated with the Betchov-Da Rios equation, we obtain the derivative formulas of an extended Darboux frame field of a unit speed curve u-parameter curve Ω=Ω(u,v) for all v. Also, we get the geometric invariants k and h of the soliton surface Ω=Ω(u,v) and we obtain the Gaussian curvature, mean curvature vector and Gaussian torsion of Ω. We give some important geometric characterizations such as flatness, minimality and semi-umbilicaly with the aid of these invariants. Additionally, we study the curvature ellipse of the Betchov-Da Rios soliton surface and Wintgen ideal (superconformal) Betchov-Da Rios soliton surface with respect to an extended Darboux frame field. Finally, we construct an application for the Betchov-Da Rios soliton surface with the aid of an extended Darboux frame field.