Related papers: A shadowing lemma for abelian Higgs vortices
We consider the noncommutative Abelian-Higgs theory and investigate general static vortex configurations including recently found exact multi-vortex solutions. In particular, we prove that the self-dual BPS solutions cease to exist once the…
On a smooth line bundle $L$ over a compact K\"ahler Riemann surface $\Sigma$, we study the family of vortex equations with a parameter $s$. For each $s \in [1,\infty]$, we invoke techniques in \cite{Br} by turning the $s$-vortex equation…
This paper deals with isothermal Euler-Poisson system which is used to model collapse of self-gravitating Newtonian star. Density dependent viscosity term is added on the right-hand side of momentum equation and it has been proved that…
We explore the characteristics of shadows for a general class of spherically symmetric, static spacetimes, which may arise in general relativity or in modified theories of gravity. The chosen line element involves a sum (with constant but…
This article sets forth results on the existence, a priori estimates and boundedness of positive solutions of a singular quasilinear systems of elliptic equations involving variable exponents. The approach is based on Schauder's fixed point…
Using the Hamilton-Jacobi method, we study certain optical shadows of rotating Bardeen-AdS black holes in the presence of internal and external field contributions. Precisely, we examine the shadow using one-dimensional real curves. By…
Irrotational relativistic vortex configurations in uniform subsonic motion with respect to a surrounding perfect fluid are analysed for the purpose of application to superfluid layers in neutron stars. Asymptotic solutions are found by…
By considering full-field string solutions of the Abelian--Higgs model, we modify the model of a fluid of strings (which is composed of Nambu strings) to obtain a model for a ``fluid of vortices.'' With this model, and following closely…
We study self-dual multi-vortex solutions of Chern-Simons Higgs theory in a background curved spacetime. The existence and decaying property of a solution are demonstrated.
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 this paper, we use Legendre-Fenchel transform and a space decomposition to carry out Fountain theorem and dual Fountain theorem for the following elliptic system of Hamiltonian type: \[ \begin{cases} \begin{aligned} -\Delta u&=H_v(u, v)…
A variation on the abelian Higgs model, with global SU(2) x local U(1) symmetry broken to global U(1) was recently shown by Vachaspati and Achucarro to admit stable, finite energy cosmic string solutions even though the manifold of minima…
Cosmic strings are considered in two types of gauged sigma models, which generalize the gravitating Abelian Higgs model. The two models differ by whether the U(1) kinetic term is of the Maxwell or Chern-Simons form. We obtain the…
Let $G=(V,E)$ be a connected finite graph. We study the relativistic non-Abelian Chern-Simons-Higgs vortex equations on the graph $G$. We establish an existence result to the relativistic non-Abelian Chern-Simons-Higgs vortex equations.
We derive the Bogomol'nyi equations in generalized Abelian Higgs theories which allow the coexistence of vortices and antivortices over a compact Riemann surface or the full plane. In the compact surface situation, we obtain a necessary and…
We establish quantitative asymptotic behavior of positive solutions of a family of nonlinear elliptic equations on the half cylinder near the end. This unifies the study of isolated singularities of some semilinear elliptic equations, such…
In this paper we establish a multiplicity result concerning the existence of doubly periodic solutions for a $2\times2$ nonlinear elliptic system arising in the study of self-dual non-Abelian Chern--Simons vortices. We show that the given…
New solutions to the abelian U(1) Higgs model, corresponding to vortices of integer and half-integer winding number bound onto the edges of domain walls and possibly surrounded by annular current flows, are described, based on a…
The low energy dynamics of vortices in selfdual Abelian Higgs theory is of second order in vortex velocity and characterized by the moduli space metric. When Chern-Simons term with small coefficient is added to the theory, we show that a…
We study a class of fully nonlinear elliptic equations on closed Hermitian manifolds. We derive $C^\infty$ {\em a priori} estimates, and then prove the existence of admissible solutions. In the approach, a new Hermitian metic is constructed…