Related papers: Point vortices on the sphere: a case with opposite…
We study magnetic vortex-like solutions lying on the spherical surface. The simplest cylindrically symmetric vortex presents two cores (instead of one, like in open surfaces) with same charge, so repealing each other. However, the net…
We get point vortices dynamics equations on a rotating sphere surface directly from the hydrodynamic equations as representing their weak exact solution contrary to the conventional case of the use of a kinematic relationship between a…
This paper investigates the vortex confinement property of the two-point vortex system in a planar domain. We compute the time over which initial point vortices around a stable stationary point remain within a slightly larger ball. In…
The structure and stability of various vortices in F=1 spinor Bose-Einstein condensates are investigated by solving the extended Gross-Pitaevskii equation under rotation. We perform an extensive search for stable vortices, considering both…
Stable assemblages of localized vortices exist which have particle-like properties, such as mass, and which can interact with one another when they closely approach. In this article I calculate the mass of these localized states and…
We show that the invariant measure of point vortices, when conditioning the Hamiltonian to a finite interval, converges weakly to the enstrophy measure by conditioning the renormalized energy to the same interval. We also prove the…
We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the two-dimensional (2D) cubic-quintic nonlinear Schr{\"o}dinger equation. We develop a semi-analytical approach,…
We present for the first time solutions in the gauged $U(1)\times U(1)$ model of Witten describing vortons -- spinning flux loops stabilized against contraction by the centrifugal force. Vortons were heuristically described many years ago,…
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. The main result concerns the global existence of…
In this paper, we construct a family of global solutions to the incompressible Euler equation on a standard 2-sphere. These solutions are odd-symmetric with respect to the equatorial plane and rotate with a constant angular speed around the…
We study both analytically and numerically the existence, uniqueness, and stability of vortex and dipole vector solitons in a saturable nonlinear medium in (2+1) dimensions. We construct perturbation series expansions for the vortex and…
We have studied numerically the Hamiltonian dynamics of two same-sign point vortices in an effectively two-dimensional, harmonically trapped Bose-Einstein condensate. We have found in the phase space of the system an impenetrable wall that…
In this paper we prove the existence of vortices, namely standing waves with non null angular momentum, for the nonlinear Klein-Gordon equation in dimension $N\geq 3$. We show with variational methods that the existence of these kind of…
We study the stability and structure of vortices emerging in two-dimensional quantum dots in high magnetic fields. Our results obtained with exact diagonalization and density-functional calculations show that vortex structures can be found…
Topological point defects on orientationally ordered spheres, and on deformable fluid vesicles have been partly motivated by their potential applications in creating super-atoms with directional bonds through functionalization of the…
We study a special kind of singular vorticities in ideal 2D fluids that combine features of point vortices and vortex sheets, namely pointed vortex loops. We focus on the coadjoint orbits of the area-preserving diffeomorphism group of…
We examine the existence and stability of nonlinear discrete vortex solitons in a square lattice when the standard discrete Laplacian is replaced by a fractional version. This creates a new, effective site-energy term, and a coupling among…
It is well known that the two-dimensional (2D) nonlinear Schr\"odinger equation (NLSE) with the cubic-quintic (CQ) nonlinearity supports a family of stable fundamental solitons, as well as solitary vortices (alias vortex rings), which are…
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…
We present experimental and theoretical results on formation of quantum vortices in a laser beam propagating in a nonlinear medium. Topological constrains richer than the mere conservation of vorticity impose an elaborate dynamical behavior…