Vortex filament equation for a regular polygon

Francisco de la Hoz, Luis Vega

Type: Article

Publication Date: 2014-11-14

Citations: 27

DOI: https://doi.org/10.1088/0951-7715/27/12/3031

Abstract

In this paper, we study the evolution of the vortex filament equation, with X(s, 0) being a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give strong evidence that X(s, t) is also a polygon at any rational time; moreover, it can be fully characterized, up to a rigid movement, by a generalized quadratic Gauß sum.

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