Li, YanlinErdoğdu, MelekYavuz, Ayşe2023-05-182023-05-182023Li, Y., Erdoğdu, M., Yavuz, A. (2023). Differential geometric approach of Betchov-Da Rios soliton equation. Hacettepe Journal of Mathematics and Statistics, 52, 1, 114-125.2651-477Xhttp://dx.doi.org/10.15672/hujms.1052831https://hdl.handle.net/20.500.12452/9644MakaleWOS:000964265900009PubMed ID:35296227In the present paper, we investigate differential geometric properties the soliton surface M associated with Betchov-Da Rios equation. Then, we give derivative formulas of Frenet frame of unit speed curve 4) = 4)(s, t) for all t. Also, we discuss the linear map of Weingarten type in the tangent space of the surface that generates two invariants: k and h. Moreover, we obtain the necessary and sufficient conditions for the soliton surface associated with Betchov-Da Rios equation to be a minimal surface. Finally, we examine a soliton surface associated with Betchov-Da Rios equation as an application. Mathematics Subject Classification (2020). 35Q55, 53A05eninfo:eu-repo/semantics/openAccessBetchov-Da Rios EquationLocalized İnduction Equation (LIE)Smoke Ring EquationVortex Filament EquationNonlinear Schrodinger (NLS) EquationDifferential geometric approach of Betchov-Da Rios soliton equationArticle52111412535296227Q3WOS:00096426590000910.15672/hujms.1052831