Related papers: Vortex solutions of the Popov equations
We review the current status of the problem of constructing classical field theory solutions describing stationary vortex rings in Minkowski space in 3+1 dimensions. We describe the known up to date solutions of this type, such as the…
We consider the Yang-Mills instanton equations on the four-dimensional manifold S^2xSigma, where Sigma is a compact Riemann surface of genus g>1 or its covering space H^2=SU(1,1)/U(1). Introducing a natural ansatz for the gauge potential,…
In this work we consider an Abelian O(3) sigma model coupled nonminimally with a gauge field governed by a Maxwell and Chern-Simons terms. Bogomol'nyi equations are constructed for a specific form of the potential and generic nonminimal…
We construct explicit multivortex solutions for the first and second complex sine-Gordon equations. The constructed solutions are expressible in terms of the modified Bessel and rational functions, respectively. The vorticity-raising and…
A quantized vortex in the Bose-Einstein condensation (BEC), which is known to be unstable intrinsically, is demonstrated theoretically to be stabilized by the finite temperature effect. The mean-field calculation of Popov approximation…
We have found several families of vortex soliton solutions in two-dimensional discrete dissipative systems governed by the cubic-quintic complex Ginzburg-Landau equation. There are symmetric and asymmetric solutions, and some of them have…
By imposing self-duality conditions, we obtain the explicit form in which gauge theories spontaneously breakdown in the Bogomol'nyi limit. In this context, we reconsider the Abelian Higgs, Chern-Simons Higgs and Maxwell-Chern-Simons Higgs…
We demonstrate that integrable abelian vortex equations on constant curvature Riemann surfaces can be reinterpreted as flat non-abelian Cartan connections. By lifting to three dimensional group manifolds we find higher dimensional analogues…
We deal with the Hill's spherical vortex, which is an exact solution to the Euler equation, and manage the solution to satisfy the incompressible Navier-Stokes(INS) equations with a viscous term. Once we get a viscous solution to the INS…
In this article, we first consider solutions to a semilinear elliptic problem in divergence form \begin{equation*} \begin{cases} -\varepsilon^2\text{div}(K(x)\nabla u)= (u-q|\ln\varepsilon|)^{p}_+,\ \ &x\in \Omega,\\ u=0,\ \ &x\in\partial…
We produce examples of solutions to the non-abelian gravitating vortex equations, which are a dimensional reduction of the K\"aher-Yang-Mills- Higgs equations. These are equations for a K\"ahler metric and a metric on a vector bundle. We…
We study topologically stable non-Abelian global vortices in the U(N) linear sigma model. The profile functions of the solutions are numerically obtained. We investigate the behaviour of vortices in two limits in which masses of traceless…
Following our paper [J. Math. Phys. 50 (2009) 123102], we systematically carry out Lie symmetry analysis for the barotropic vorticity equation on the rotating sphere. All finite-dimensional subalgebras of the corresponding maximal Lie…
The N-vortex solutions to the two-dimensional Ginzburg - Landau equations for the kappa=1/\sqrt(2) parameter are built. The exact solutions are derived for the vortices with large numbers of the magnetic flux quanta. The size of vortex core…
We consider Riemann surfaces obtained from nodal curves with infinite cylinders in the place of nodal and marked points, and study the space of finite energy vortices defined on these surfaces. To compactify the space of vortices, we need…
We show that Abelian Higgs Models with dielectric function defined on the noncommutative plane enjoy self-dual vorticial solutions. By choosing a particular form of the dielectric function, we provide a family of solutions whose Higgs and…
In this work, a Maxwell-Higgs system is coupled to a neutral scalar field that engenders $Z_2$ symmetry. At critical coupling, the resulting field equations may be identified with those of a Maxwell-Higgs model doped with an impurity whose…
New exact spatially localized stationary solutions against the background of a zonal flow are found for the (3+1)-dimensional nonlinear non-dissipative quasi-geostrophic potential vorticity equation, which describes Rossby waves and…
We investigate the presence of vortices in generalized Maxwell-Higgs models with a hidden sector. The model engenders $U(1)\times U(1)$ symmetry, in a manner that the sectors are coupled via the visible magnetic permeability depending only…
In this paper we derive the equations of motion for two-layer point vortex motion on the upper half plane. We study the invariants using symmetry, including the Hamiltonian and show that the two vortex problem is integrable. We characterize…