Abstract
The main scope of this paper is to examine the smoke ring (or vortex filament) equation which can be viewed as a dynamical system on the space curve in E³. The differential geometric properties the soliton surface accociated with Nonlinear Schrödinger (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 τ_{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.
Highlights
Investigation of motion of a vortex ...lament provides the crucial problems of mathematical physics and di¤erential geometry
The main scope of this paper is to examine the smoke ring equation which can be viewed as a dynamical system on the space curve in E3: The di¤erential geometric properties the soliton surface associated with Nonlinear Schrödinger (NLS) equation, which is called NLS surface or Hasimoto surface, are investigated by using Darboux frame
We give a di¤erent proof of that the s parameter curves of NLS surface are the geodesics of the soliton surface
Summary
Investigation of motion of a vortex ...lament provides the crucial problems of mathematical physics and di¤erential geometry. It can be considered that these vortex motions, which involve no change of form, correspond to traveling wave solutions of the Nonlinear Schrödinger (NLS) equation, [14] These kind of soliton surfaces that are associated with the NLS equation are called NLS surfaces or Hasimoto surfaces. Di¤erential geometric properties of the soliton surfaces associated with NLS equation are obtained. The NLS equation of repulsive type for timelike curves and nonlinear heat system were examined in a general intrinsic geometric setting including a normal congruence in 3-dimensional Minkowski space in the study [5]. We investigate di¤erential geometric properties of the soliton surface associated with Nonlinear Schrödinger (NLS) equation, which is called NLS surface or Hasimoto surface, are investigated by using the Darboux frame.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
