Finite-Gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations |
| |
Authors: | A Calini T Ivey |
| |
Institution: | (1) Department of Mathematics, College of Charleston, Charleston, SC 29424, USA |
| |
Abstract: | 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|