Vortices and Polynomials

Clarkson, Peter (2009) Vortices and Polynomials. Studies in Applied Mathematics, 123 (1). pp. 37-62. ISSN 0022-2526 . (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1111/j.1467-9590.2009.00446.x

Abstract

The relationship between point vortex dynamics and the properties of polynomials with roots at the vortex positions is discussed. Classical polynomials, such as the Hermite polynomials, have roots that describe the equilibria of identical vortices on the line. Stationary and uniformly translating vortex configurations with vortices of the same strength but positive or negative orientation are given by the zeros of the Adler–Moser polynomials, which arise in the description of rational solutions of the Korteweg–de Vries equation. For quadrupole background flow, vortex configurations are given by the zeros of polynomials expressed as Wronskians of Hermite polynomials. Further, new solutions are found in this case using the special polynomials arising in the description of rational solutions of the fourth Painlevé equation.

Item Type: Article
Additional information: Proceedings Paper Conference Information: International Conference on Nonlinear Waves - Theory and Application Beijing,China, June 9-12th 2008
Subjects: Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Peter A Clarkson
Date Deposited: 25 Sep 2009 08:36
Last Modified: 14 May 2014 13:56
Resource URI: http://kar.kent.ac.uk/id/eprint/20510 (The current URI for this page, for reference purposes)
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