Related papers: Rings and Balls
Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological…
In theories where spacetime is a direct product of Minkowski space ($M^4$) and a d dimensional compact space ($K^d$), there can exist topological solitons that simultaneously wind around $R^3$ (or $R^2$ or $R^1$) in $M^4$ and the compact…
The existence of ring-like and knotted solitons in O(3) non-linear sigma model is analysed. The role of isotopy of knots/links in classifying such solitons is pointed out. Appearance of torus knot solitons is seen.
Ball lightning is one of the most mysterious atmospheric phenomena, whose long lifetime, penetrative ability, and stability are difficult to explain with traditional physical models. This paper proposes a novel theoretical framework,…
Dynamics of interaction of topological solitons (vortices) in (2+1)-dimensional O(3) nonlinear sigma model in anisotropic case are investigated. By numerical simulation methods is shown that the changes of rotation frequency of isotopic…
We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy.…
We construct an infinite number of exact time dependent soliton solutions, carrying non-trivial Hopf topological charges, in a 3+1 dimensional Lorentz invariant theory with target space S^2. The construction is based on an ansatz which…
The topology of orientable (2 + 1)d spacetimes can be captured by certain lumps of non-trivial topology called topological geons. They are the topological analogues of conventional solitons. We give a description of topological geons where…
Two topological issues on membranes in M-theory are studied: (1) Soliton is an important subject in M-theory. Under the framework of obstruction theory with the help from framed links in $S^3$, we give a complete enumeration of topological…
It is shown that the Topological Massive and ``Self-dual'' theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically…
Here we consider an interplay between the topology of the magnetization texture (which is a topological soliton, or Skyrmion) in a planar magnetic nano-element and the topology of the element itself (its connectivity). We establish the…
We discuss (2+1)-dimensional gapless surface theories of bulk (3+1)-dimensional topological phases, such as the BF theory at level $\mathrm{K}$, and its generalization. In particular, we put these theories on a flat (2+1) dimensional torus…
We present and study new non-topological soliton solutions in the $U(1)$ gauged non-linear $O(3)$ sigma model with a symmetry breaking potential in 3+1 dimensional flat space-time. The configurations are endowed with an electric and…
The first analytic topologically non-trivial solutions in the (3+1)-dimensional gauged non-linear sigma model representing multi-solitons at finite volume with manifest ordered structures generating their own electromagnetic field are…
Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known…
The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…
This work concerns scalar field theories with topologically nontrivial vacuum manifold in rotationally symmetric backgrounds of arbitrary dimension. Lagrangians with canonical and generalized kinetic terms are considered, and a Bogomol'nyi…
The nonlinear O(3) sigma-model in (2+1) dimensions with an additional potential term admits solutions called Q-lumps, having both topological and Noether charges. We consider in 3+1-dimensional spacetime the theory with Q-lumps on a domain…
By means of the variational method and numerical simulations, we demonstrate the existence of stable 3D nonlinear modes, viz. vortex ``bullets'', in the form of pulsed beams carrying orbital angular momentum, that can self-trap in a 2D…
In this report, fundamental educational concepts of linear and non-linear equations and solutions of nonlinear equations from the book High-Temperature Superconductivity: The Nonlinear Mechanism and Tunneling Measurements (Kluwer Academic…