Related papers: Five-dimensional Monopole Equation with Hedge-Hog …
Procedure of finding of the Bogomolny-Prasad-Sommerfield monopole solutions in the Georgi-Glashow model is investigated in detail on the backgrounds of three space models of constant curvature: Euclid, Riemann, Lobachevski's. Classification…
We apply a generalized field ansatz to describe the spherically symmetric sector of classical solutions of the electroweak theory. This sector contains Abelian magnetic monopoles labeled by their magnetic charge $n=\pm 1,\pm 2,\ldots$, the…
We show that in certain non-Abelian Born-Infeld-Higgs theories there are monopole solutions obeying Bogomol'nyi-like equations in the Prasad-Sommerfield limit. We also discuss the existence of instanton solution in an SU(2) Born-Infeld…
New static regular axially symmetric solutions of SU(2) Yang-Mills-Higgs theory are constructed. They are asymptotically flat and represent gravitating monopole-monopole pairs. The solutions form two branches linked to the second…
In this paper the two dimensional abelian Higgs model is revisited. We show that in the physical sector, the solutions to the Euler-Lagrange equations include solitons.
We prove the existence of infinitely many solutions to a class of non-symmetric Dirichlet problems with exponential nonlinearities. Here the domain $\Omega \subset\subset \mathbb{R}^{2l}$ where $2l$ is the order of the equation. Considered…
A generalized flux problem with Abelian and non-Abelian fluxes is considered. In the Abelian case we shall show that the generalized flux problem for tight-binding models of noninteracting electrons on either $2n$ or $2n+1$ dimensional…
A continuum of monopole, dyon and black hole solutions exist in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space. Their structure is studied in detail. The solutions are classified by non-Abelian electric and magnetic…
We consider four-dimensional Omega-deformed N=2 supersymmetric SU(2) gauge theory on A1 space and its lift to five dimensions. We find that the partition functions can be reproduced via special geometry and the holomorphic anomaly equation.…
It is shown that a canonical geometric setting of the integrable TED equation is a Kahlerian tangent bundle of an affine manifold. The remarkable multi-dimensional consistency of this 4+4-dimensional dispersionless partial differential…
Anisotropic exponential cosmological solutions for a space of arbitrary dimension filled with ordinary matter in the 4th and 5th orders of Lovelock gravity are obtained. Also we have supposed a generalization of such solutions on an…
We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…
Using the generalized symmetry method we finish a classification, started in the article [R.N. Garifullin, R.I. Yamilov and D. Levi, Classification of five-point differential-difference equations, J. Phys. A: Math. Theor. 50 (2017) 125201…
We review the Bogomol'nyi equations and investigate an alternative route in obtaining it. It can be shown that the known BPS equations can be derived directly from the corresponding Euler-Lagrange equations via separation of variables,…
The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…
An examples of Monge-Ampere equations connected with six-dimensional generalization of the Plebanski four-dimensional space are considered. Their particular solutions are constructed.
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…
We present a list of (1+1)-dimensional second-order evolution equations all connected via a proposed generalised hodograph transformation, resulting in a tree of equations transformable to the linear second-order autonomous evolution…
We demonstrate that the four (3 + 1)-dimensional free Abelian 2-form gauge theory presents a tractable field theoretical model for the Hodge theory where the well-defined symmetry transformations correspond to the de Rham cohomological…
We show that any classical solution of the diffusive Hamilton-Jacobi (DHJ) equation $-\Delta u= |\nabla u|^p$ in a half-space with zero boundary conditions for $1<p\le 2$ is necessarily one-dimensional. This improves the previously known…