Erdogdu, MelekYavuz, Ayse2024-02-232024-02-2320211303-5991https://doi.org/10.31801/cfsuasmas.724634https://hdl.handle.net/20.500.12452/15717The main scope of this paper is to examine the smoke ring (or vortex flament) equation which can be viewed as a dynamical system on the space curve in E-3: The differential geometric properties the soliton surface associated with Nonlinear Schrodinger (NLS) equation, which is called NLS surface or Hasimoto surface, are investigated by using Darboux frame. Moreover, Gaussian and mean curvature of Hasimoto surface are found in terms of Darboux curvatures k(n), k(g) and tau(g). Then, we give a different proof of that the s-parameter curves of NLS surface are the geodesics of the soliton surface. As applications we examine two NLS surfaces with Darboux Frame.eninfo:eu-repo/semantics/openAccessSmoke Ring EquationVortex Flament EquationNls SurfaceDarboux FrameArticle701510521WOS:00066338390003110.31801/cfsuasmas.724634