ABSTRACT:
In this talk I will discus the relationship between vortex dynamics and properties of polynomials with roots at the vortex positions. Classical polynomials such as the Hermite and Laguerre polynomials have roots which describe vortex equilibria. Stationary vortex configurations with vortices of the same strength and positive or negative configurations are located at the roots of the Adler-Moser polynomials, which are associated with rational solutions of the Kortweg-de Vries equation. Aref [Fluid Dyn. Res., 39 (2007) 5–23; J. Math. Phys., 48
(2007) 065401] remarks that the relationship between vortex dynamics and the KdV equation is “quite unexpected and very beautiful”. I will also discuss the polynomials associated with rational solutions of other soliton equations such as the Boussinesq and nonlinear Schr ̈ dinger equations, and the motion of the poles of rational solutions of these equations.
ADDITIONAL INFORMATION:
Peter’s research interests include soliton theory, Painleve equations and analysis, asymptotics, Backlund transformations, orthogonal polynomials and special functions, symmatry reductions.
http://www.kent.ac.uk/smsas/personal/pac3/