@article{article_1052831, title={Differential geometric approach of Betchov-Da Rios soliton equation}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={52}, pages={114–125}, year={2023}, DOI={10.15672/hujms.1052831}, author={Li, Yanlin and Erdoğdu, Melek and Yavuz, Ayşe}, keywords={Betchov-Da Rios equation, localized induction equation (LIE), smoke ring equation, vortex filament equation, nonlinear Schrodinger (NLS) equation}, abstract={In 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 $\Phi=\Phi(s,t)$ 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.}, number={1}, publisher={Hacettepe University}, organization={National Natural Science}