This paper deals with the existence of N vortex patches located at the vertex of a regular
polygon with N sides that rotate around the center of the polygon at a constant angular …

This paper considers two point boundary value problems for conservative systems defined
in multiple coordinate systems, and develops a flexible a posteriori framework for computer …

Helhmoltz–Kirchhoff equations of motions of vortices of an incompressible fluid in the plane
define a dynamics with singularities and this leads to a Zermelo navigation problem …

We examine the motion of N symmetric hetons (oppositely signed vertical dipoles) in a two-
layer quasi-geostrophic model. We consider the special case of N-fold symmetry in which …

We develop a systematic approach for proving the existence of choreographic solutions in
the gravitational n body problem. Our main focus is on spatial torus knots: that is, periodic …

This paper seeks and examines N-symmetric vortical solutions of the two-layer geostrophic
model for the special case when the vortices (or eddies) have vanishing summed strength …

We study the existence, stability, and dynamics of vortex dipole and quadrupole
configurations in the nonlinear Schrödinger (NLS) equation on the surface of a torus. For this …

We consider the $ N $-vortex problem on the sphere assuming that all vorticities have equal
strength. We investigate relative equilibria (RE) consisting of $ n $ latitudinal rings which are …

This paper gives an analysis of the movement of n vortices on the sphere. When the vortices
have equal circulation, there is a polygonal solution that rotates uniformly around its center …

We consider the N-vortex problem on the sphere assuming that all vortices have equal
strength. We develop a theoretical framework to analyse solutions of the equations of motion …