Differential geometric aspects of nonlinear Schrödinger equation

Authors : Melek ERDOĞDU, Ayşe YAVUZ

Pages : 510-521

Doi:10.31801/cfsuasmas.724634

View : 9 | Download : 7

Publication Date : 2021-06-30

Article Type : Research Paper

Abstract :The main scope of this paper is to examine the smoke ring insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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.
Keywords : Smoke ring equation, Vortex Filament equation, NLS surface, Darboux Frame