Related papers: Vortex solutions of the Popov equations
We consider the Gross-Pitaevskii equation with a confining ring potential with a Gaussian profile. By introducing a rotating sinusoidal perturbation, we numerically highlight the nucleation of quantum vortices in a particular regime…
It is shown that both the sinh--Gordon equation and the elliptic Tzitzeica equation can be interpreted as the Taubes equation for Abelian vortices on a CMC surface embedded in $\R^{2, 1}$, or on a surface conformally related to a hyperbolic…
Heisenberg-like spins lying on the pseudosphere (a 2-dimensional infinite space with constant negative curvature) cannot give rise to stable soliton solutions. Only fractional solutions can be stabilized on this surface provided that at…
Vortices are considered in relativistic Maxwell-Higgs systems in interaction with a neutral scalar field. The gauge field interacts with the neutral field via the presence of generalized permeability, and the charged and neutral scalar…
In this work we found the new class of exact stationary solutions for 2D-Euler equations. Unlike of already known solutions, the new one contain complex singularities. We consider as complex, point singularities which have the vector field…
We consider the problem of finding a solution to the incompressible Euler equations $$ \omega_t + v\cdot \nabla \omega = 0 \quad \hbox{ in } \mathbb{R}^2 \times (0,\infty), \quad v(x,t) = \frac 1{2\pi} \int_{{\mathbb R}^2} \frac…
Helmholtz's equations provide the motion of a system of N vortices which describes a planar incompressible fluid with zero viscosity. A relative equilibrium is a particular solution of these equations for which the distances between the…
The thermodynamics of vortices in the critically coupled abelian Higgs model, defined on the plane, are investigated by placing $N$ vortices in a region of the plane with periodic boundary conditions: a torus. It is noted that the moduli…
We introduced a generalized Maxwell-Higgs model in a $(3+1)$ isotropic spacetime, and we found their stationary solutions using the BPS approach in curved spacetime. In order to investigate the compact-like vortices, we assume a particular…
For the $2D$ Euler equation in vorticity formulation, we construct localized smooth solutions whose critical Sobolev norms become large in a short period of time, and solutions which initially belong to $L^\infty \cap H^1$ but escapes $H^1$…
We deal with planar vortex structures in Maxwell-Higgs models in the presence of a generalized magnetic permeability. The model under investigation engenders a real parameter that controls the behavior of the tail of the solutions and of…
In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…
The specific geometry of a strip provides connections between solitons and solitonic vortices, which are vortices with a solitonic behaviour in the infinite direction of the strip. We show that there exist stationary solutions to the…
We construct families of ordinary and gap solitons (GSs), including solitary vortices, in the two-dimensional (2D) system based on the nonlinear-Schr\"Aodinger/Gross-Pitaevskii equation with the 2D or quasi-1D (Q1D) periodic linear…
We obtain both topological as well as nontopological self-dual charged vortex solutions of finite energy per unit length in a generalized abelian Higgs model in $3+1$ dimensions. In this model the Bogomol'nyi bound on the energy per unit…
There exists a class of gauge models incorporating a finite density of matter in which the Higgs mechanism is provided by condensates of gauge (or gauge and scalar) fields, i.e., there are vector condensates in this case. We describe vortex…
A consistent BPS formalism to study the existence of topological axially symmetric vortices in generalized versions of the Born-Infeld-Higgs electrodynamics is implemented. Such a generalization modifies the field dynamics via introduction…
The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…
The inhomogeneous abelian Higgs model with a magnetic impurity in the BPS limit is studied for both relativistic and nonrelativistic regimes. Though the symmetry of spatial translation is broken by inhomogeneity, extension to an…
We discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism. At critical self-coupling, and for low temperatures, it has been argued that the configuration space for vortex dynamics in each topological class…