Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

Details Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

2006-12-29

arxiv.org/abs/nlin/0612065v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

33 pages, 5 figures; submitted to Journal of Nonlinear Science

Scientific paper

10.1007/s00332-007-9002-x

We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.

Affiliated with

Also associated with

No associations

Rating

Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations 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 Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-380103