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Vortices ans Polynomials: Nonuniqueness of the Adler-Moser polynomials for the Tkachenko equation | | Maria V. Demina
; Nikolay A. Kudryashov
; | | Date: |
19 Dec 2011 | | Abstract: | Stationary and translating relative equilibria of point vortices in the plane
are studied. It is shown that stationary equilibria of a system containing
point vortices with arbitrary choice of circulations can be described with the
help of the Tkachenko equation. It is obtained that the Adler - Moser
polynomial are not unique polynomial solutions of the Tkachenko equation. A
generalization of the Tkachenko equation to the case of translating relative
equilibria is derived. It is shown that the generalization of the Tkachenko
equation possesses polynomial solutions with degrees that are not triangular
numbers. | | Source: | arXiv, 1112.4350 | | Services: | Forum | Review | PDF | Favorites | |
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