Related papers: Generalized Jacobi Elliptic One-Monopole - Type A
We investigate a generalization of Hopf algebra $\mathfrak{sl}_{q}(2)$ by weakening the invertibility of the generator $K$, i.e. exchanging its invertibility $KK^{-1}=1$ to the regularity $K\overline{K}K=K$. This leads to a weak Hopf…
The possible actions of symmetry groups on generalized Higgs fields coupled to an Einstein-Yang-Mills field are studied with differential geometrical techniques involving principal and associated bundles. A classification of conjugacy…
We discuss new exact spherically symmetric static solutions to non-minimally extended Einstein-Yang-Mills equations. The obtained solution to the Yang-Mills subsystem is interpreted as a non-minimal Wu-Yang monopole solution. We focus on…
We study isolated singularities of two dimensional Yang-Mills-Higgs fields defined on a fiber bundle, where the fiber space is a compact Riemannian manifold and the structure group is a compact connected Lie group. In general the…
In this paper we study (static) solutions of the rank 2 Yang-Mills-Higgs equations on the Riemann sphere, with concical singularities, that bifurcate from constant curvature connections. We focus attention on the case where there are…
In this paper, we study the convergence of Yang-Mills-Higgs fields defined on fiber bundles over Riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the Riemann surface is allowed to vary. We…
Jacobian elliptic travelling wave solutions for a new Hamiltonian amplitude equation determining some instabilities of modulated wave train are obtained. By mere variation of the Jacobian elliptic parameter $k^2$ from zero to one, these…
We study monotonicity and 1-dimensional symmetry for positive solutions with algebraic growth of the following elliptic system: \[ \begin{cases} -\Delta u = -u v^2 & \text{in $\R^N$}\\ -\Delta v= -u^2 v & \text{in $\R^N$}, \end{cases} \]…
For three conspicuous gauge groups, namely, SU(2), SU(3) and SO(5), and at first order in the noncommutative parameter matrix h\theta^{\mu\nu}, we construct smooth monopole --and, some two-monopole-- fields that solve the noncommutative…
Let $(M,g)$ be a compact Riemannian manifold of dimension $n\geq 3$. Under some assumptions, we prove that there exists a positive function $\varphi$ solution of the following Yamabe type equation \Delta \varphi+ h\varphi= \tilde h…
We compute solutions to the Hermitian Yang-Mills equations on holomorphic vector bundles $V$ via an alternating optimisation procedure founded on geometric machine learning. The proposed method is fully general with respect to the rank and…
We give a detailed path integral derivation of the elliptic genus of a supersymmetric coset conformal field theory, further twisted by a global U(1) symmetry. It gives rise to a Jacobi form in three variables, which is the modular…
We look for spectral type differential equations satisfied by the generalized Jacobi polynomials, which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with…
Static, spherically symmetric solutions of the Yang-Mills-Dilaton theory are studied. It is shown that these solutions fall into three different classes. The generic solutions are singular. Besides there is a discrete set of globally…
We study classical solutions in the SU(2) Einstein-Yang-Mills-Higgs theory. The spherically symmetric ans\"atze for all fields are given and the equations of motion are derived as a system of ordinary differential equations. The asymptotics…
In this paper, under very general assumptions, we prove existence and regularity of distributional solutions to homogeneous Dirichlet problems of the form $$\begin{cases} \displaystyle - \Delta_{1} u = h(u)f & \text{in}\, \Omega,\newline…
We have found exact, periodic, time-dependent solitary wave solutions of a discrete $\phi^4$ field theory model. For finite lattices, depending on whether one is considering a repulsive or attractive case, the solutions are either Jacobi…
We describe new solutions of Yang-Mills-Higgs theories consisting of magnetic monopoles in a phase with fully broken gauge symmetry. Rather than spreading out radially, the magnetic field lines form flux tubes. The solution is topologically…
We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to the classical weight function for the Jacobi polynomials together with point masses at both…
A proof is given of Polyakov conjecture about the accessory parameters of the SU(1,1) Riemann-Hilbert problem for general elliptic singularities on the Riemann sphere. Its relevance to 2+1 dimensional gravity is stressed.