Point vortices and classical orthogonal polynomials

Details Point vortices and classical orthogonal polynomials Point vortices and classical orthogonal polynomials

2012-01-17

arxiv.org/abs/1201.3481v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

20 pages, 12 figures

Scientific paper

Stationary equilibria of point vortices with arbitrary choice of circulations in a background flow are studied. Differential equations satisfied by generating polynomials of vortex configurations are derived. It is shown that these equations can be reduced to a single one. It is found that polynomials that are Wronskians of classical orthogonal polynomials solve the latter equation. As a consequence vortex equilibria at a certain choice of background flows can be described with the help of Wronskians of classical orthogonal polynomials.

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