Differential geometric aspects of nonlinear Schrödinger equation
| Autor: | Melek Erdoğdu, Ayşe Yavuz |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
symbols.namesake Nonlinear Sciences::Exactly Solvable and Integrable Systems Matematik Uygulamalı Mathematics::Analysis of PDEs Smoke ring equation Vortex Filament equation NLS surface Darboux Frame Mathematics Applied symbols General Medicine Nonlinear Sciences::Pattern Formation and Solitons Nonlinear Schrödinger equation Differential (mathematics) Mathematical physics |
| Zdroj: | Volume: 70, Issue: 1 510-521 Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics |
| ISSN: | 1303-5991 2618-6470 |
| DOI: | 10.31801/cfsuasmas.724634 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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