Point vortices and classical orthogonal polynomials
Exactly Solvable and Integrable Systems
2015-06-03 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1201.3481,
title = {Point vortices and classical orthogonal polynomials},
author = {Maria V. Demina and Nikolay A. Kudryashov},
journal= {arXiv preprint arXiv:1201.3481},
year = {2015}
}
Comments
20 pages, 12 figures