Discrete Hashimoto surfaces and a doubly discrete smokering flow

Details Discrete Hashimoto surfaces and a doubly discrete smokering flow Discrete Hashimoto surfaces and a doubly discrete smokering flow

2000-07-25

arxiv.org/abs/math/0007150v1

Mathematics

Differential Geometry

LaTeX, Online version with aditional applets available at http://www-sfb288.math.tu-berlin.de/Publications/online/smokeringsOn

Scientific paper

B\"acklund 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 Schr\"odinger 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/

Affiliated with

Also associated with

No associations

Rating

Discrete Hashimoto surfaces and a doubly discrete smokering flow does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Discrete Hashimoto surfaces and a doubly discrete smokering flow, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete Hashimoto surfaces and a doubly discrete smokering flow will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-406772