Standing Waves of Fixed Period for n+1 Vortex Filaments

The n + 1 vortex filament problem has explicit solutions consisting of n 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...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2020-12, Vol.32 (4), p.1631-1640
Main Authors: Craig, Walter, García-Azpeitia, Carlos
Format: Article
Language:English
Subjects:
Applications of Mathematics
Configurations
Filaments
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Rotation
Standing waves
Vortex filaments
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Summary:The n + 1 vortex filament problem has explicit solutions consisting of n 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.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-019-09768-9