Related papers: Point vortices and classical orthogonal polynomial…
The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and…
Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the…
We study collinear relative equilibria of the planar four-vortex problem where three of the four vortex strengths are identical. The $S_3$ invariance obtained from the equality of vorticities is used to reduce the defining equations and…
We examine existence and stability of relative equilibria of the $n$-vortex problem specialized to the case where $N$ vortices have small and equal circulation and one vortex has large circulation. As the small circulation tends to zero,…
We investigate the presence of vortex solutions in potentials without vacuum state. The study is conducted considering Maxwell and Chern-Simons dynamics. Also, we use a first order formalism that helps us to find the solutions and their…
This paper concerns the investigation of the stability properties of relative equilibria which are rigidly rotating vortex configurations sometimes called vortex crystals, in the N-vortex problem. Such a configurations can be characterized…
This study examines the motion of spherical inertial particles in a three-dimensional rotating cylindrical vortex - a simplified model of geophysical flow structures such as oceanic eddies. The analytical vortex formulation enables the…
Fluid flows around an obstacle generate vortices which, in turn, generate lift forces on the obstacle. Therefore, even in a perfectly symmetric framework equilibrium positions may be asymmetric. We show that this is not the case for a…
Vortices (flows with closed elliptic streamlines) are exact nonlinear solutions to the compressible Euler equation. In this contribution, we use differential geometry to derive the transformations between Cartesian and elliptic coordinates,…
We present a novel method for estimating the circulations and positions of point vortices using trajectory data of passive particles in the presence of Gaussian noise. The method comprises two algorithms: the first one calculates the vortex…
We derive the proper form of Virial theorem for a system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a very simple form that can be used to obtain general results about the dynamics…
The problem of vortex pair motion in two-dimensional plane radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases…
It is shown that the hydrodynamics equations for a thin spherical liquid layer are satisfied by the stream function of a pair of antipodal vortices-APV, in contrast to the stream function of a single point vortex on a sphere with a…
Optical vortices arise as phase singularities of the light fields and are of central interest in modern optical physics. In this paper, some existence theorems are established for stationary vortex wave solutions of a general class of…
Given a regular polygonal arrangement of identical objects, turning around a central object (masses, vortices or dNLS oscillators), this paper studies the global bifurcation of relative equilibria in function of a natural parameter (central…
We study non-equilibrium polariton superfluids in the optical parametric oscillator (OPO) regime using a two-component Gross-Pitaevskii equation with pumping and decay. We identify a regime above OPO threshold, where the system undergoes…
We show that certain infinitesimal operators of the Lie-point symmetries of the incompressible 3D Navier-Stokes equations give rise to vortex solutions with different characteristics. This approach allows an algebraic classification of…
We study the behaviour of heavy inertial particles in the flow field of two like-signed vortices. In a frame co-rotating with the two vortices, we find that stable fixed points exist for these heavy inertial particles; these stable…
A theoretical analysis is presented for turbulent flows, applicable for canonical (channel, boundary-layer and free jet) geometries. Momentum and energy balance for a control volume moving at the local mean velocity decouples the…
We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation $i \partial_t u = \Delta u + {1\over \varepsilon^2} (p_\varepsilon^2(x) - |u|^2)$. For a unique scaling regime $|p_\varepsilon(x) - 1 | = O(|\log…