Standing waves of fixed period for $n+1$ vortex filaments
Analysis of PDEs
2019-03-21 v1
Abstract
The vortex filament problem has explicit solutions consisting of parallel filaments of equal circulation in the form of nested polygons uniformly rotating around a central filament which has circulation of opposite sign. We show that when the relation between temporal and spatial periods is fixed at certain rational numbers, these configurations have an infinite number of homographic time dependent standing wave patterns that bifurcate from these uniformly rotating central configurations.
Keywords
Cite
@article{arxiv.1903.08302,
title = {Standing waves of fixed period for $n+1$ vortex filaments},
author = {Walter Craig and Carlos García-Azpeitia},
journal= {arXiv preprint arXiv:1903.08302},
year = {2019}
}