Related papers: Existence of the Solution for the 't Hooft-Polyako…
We have found analytical self-dual solutions within the generalized Yang-Mills-Higgs model introduced in Phys. Rev. D 86, 085034 (2012). Such solutions are magnetic monopoles satisfying Bogomol'nyi-Prasad-Sommerfield (BPS) equations and…
In this article, we carry out the Hamiltonization in the axial gauge, of the t'Hooft-Polyakov monopole field outside the localized region, which represents the monopole's core. One feature of the treatment here, is using the Higgs vacuum…
This article concerns the global-in-time existence of smooth solutions with small amplitude to two space dimensional Euler-Poisson system. The main difficulty lies in the slow time decay $(1+t)^{-1}$ of the linear system. Inspired by Ozawa,…
We study static spherically symmetric monopole solutions in non-Abelian Einstein-Born-Infeld-Higgs model with normal trace structure. These monopoles are similar to the corresponding solution with symmetrised trace structure and are…
We construct static and time-dependent exact soliton solutions with non-trivial Hopf topological charge for a field theory in 3+1 dimensions with the target space being the two dimensional sphere S**2. The model considered is a reduction of…
We prove the existence and uniqueness of stationary spherically symmetric positive solutions for the Schr\"{o}dinger-Newton model in any space dimension $d$. Our result is based on an analysis of the corresponding system of second order…
We study the Abelian projection of an instanton in $R^3 \times S^1$ as a function of temperature (T) and non-trivial holonomic twist ($\omega$) of the Polyakov loop at infinity. These parameters interpolate between the circular monopole…
We consider the magnetic nonlinear inhomogeneous Schr\"odinger equation $$i\partial_t u -\left(-i\nabla+\frac{\alpha}{|x|^2}(-x_2,x_1)\right)^2 u =\pm|x|^{-\varrho}|u|^{p-1}u,\quad (t,x)\in \mathbb{R}\times \mathbb{R}^2,$$ where…
Stochastic Hall-magnetohydrodynamics equations on ${\mathbb{R}}^{3}$ with random forces expressed in terms of the time homogeneous Poisson random measures are considered. We prove the existence of a global martingale solution. The…
In this paper, we show the existence of magnetic monopoles in the pure $SU(2)$ Yang--Mills theory even in absence of scalar fields when the gauge-invariant mass term is introduced. This result follows from the recent proposal for obtaining…
We study the global existence of classical solutions for two-dimensional incompressible MHD system with only magnetic diffusion. By using the time-weighted lower-order energy and uniformly bounded higher-order energy estimates, we prove the…
For a monopole, the analogue of the Lorentz equation in matter is shown to be f = g (H - v cross D). Dual-symmetric Maxwell equations, for matter containing hidden magnetic charges in addition to electric ones, are given. They apply as well…
We investigate monopole solutions for the Born-Infeld Higgs system. We analyze numerically these solutions and compare them with the standard 't Hooft-Polyakov monopoles. We also discuss the existence of a critical value of beta (the…
We show that in the SU(2) Georgi-Glashow model, 't Hooft-Polyakov monopoles are produced by a classical instability in magnetic fields above the Ambjorn-Olesen critical field, which coincides approximately with the field at which Schwinger…
We establish the existence and uniqueness of solutions to stochastic 2D Navier-Stokes equations in a time-dependent domain driven by Brownian motion. A martingale solution is constructed through domain transformation and appropriate…
In this paper, we prove local existence and uniqueness for the 2D Prandtl-Hartmann regine in weighted Sobolev spaces. Our proof is based on using uniform estimates of the regularized parabolic equation and maximal principle under the…
We present a systematic exploration of a general family of effective $SU(2)$ models with an adjoint scalar. First, we discuss a redundancy in this class of models and use it to identify seemingly different, yet physically equivalent models.…
Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise are considered. The noise term depends on the unknown velocity and its spatial derivatives. The existence of a martingale…
The classical equations of motion of a charged particle in a spherically symmetric distribution of magnetic monopoles can be transformed into a system of linear equations, thereby providing a type of integrability. In the case of a single…
In this paper, we study the long time behavior of solutions of Klein-Gordon-Zakharov system. We show that there exists a solution with special characteristics, which we shall refer to as a dipole solution, that is, there exists a solution…