Discrete Hashimoto surfaces and a doubly discrete smokering flow

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Bäcklund transformations for smooth and ``space discrete'' Hashimoto surfaces are discussed and a geometric interpretation is given. It is shown that the complex curvature of a discrete space curve evolves with the discrete nonlinear Schrödinger equation (NLSE) of Ablowitz and Ladik, when the curve evolves with the Hashimoto or smoke ring flow. A doubly discrete Hashimoto flow is derived and it is shown, that in this case the complex curvature of the discrete curve obeys Ablovitz and Ladik's doubly discrete NLSE. Elastic curves (curves that evolve by rigid motion only under the Hashimoto flow) in the discrete and doubly discrete case are shown to be the same. There is an online version of this paper, that can be viewed using any recent web browser that has JAVA support enabled. It includes two additional java applets. It can be found at http://www-sfb288.math.tu-berlin.de/Publications/online/smokeringsOnline/
LaTeX, Online version with aditional applets available at http://www-sfb288.math.tu-berlin.de/Publications/online/smokeringsOnline/

Keywords

Differential Geometry, 53A05;52C99

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/59618

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0007150
 http://arxiv.org/abs/math/0007150

Collections

arXiv