For the three dimensional axisymmetric Euler flow, we construct a family of solutions with
multiple travelling vortex rings, with large speed of order O (| ln ɛ|), where ɛ> 0 is a small …

We give a survey concerning both very classical and recent results on the electrostatic
interpretation of the zeros of some well-known families of polynomials, and the interplay …

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 …

A large class of new exact solutions to the steady, incompressible Euler equation on the
plane is presented. These hybrid solutions consist of a set of stationary point vortices …

Point vortices in a two-dimensional fluid may be arranged so that all resulting vortex
velocities are identical; these are equivalent to force-free arrangements of 2D Coulomb …

Stationary and translating relative equilibria of point vortices in the plane are studied. It is
shown that stationary equilibria of any system containing point vortices with arbitrary choice …

In this paper a family of sequences of polynomials is studied that generalize the Adler–
Moser and Loutsenko polynomial sequences related to point vortex equilibria. The …

Rational solutions of the Boussinesq equation are expressed in terms of special polynomials
associated with rational solutions of the second and fourth Painlevé equations, which arise …

Rational solutions and special polynomials associated with the generalized K 2 hierarchy
are studied. This hierarchy is related to the Sawada-Kotera and Kaup-Kupershmidt …

In this paper two families of rational solutions and associated special polynomials for the
equations in the symmetric fourth Painlevé hierarchy are studied. The structure of the roots …