Related papers: Topological Compactons
The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in…
Profiles of static solitons in one-dimensional scalar field theory satisfy the same equations as trajectories of a fictitious particle in multidimensional mechanics. We argue that the structure and properties of the solitons are essentially…
Recently we proposed that K fields, that is, fields with a non-standard kinetic term, may provide a mechanism for the generation of thick branes, based on the following observations. Firstly, K field theories allow for soliton solutions…
We establish the existence of static, classically-stable, winding solitons in renormalizable three-dimensional gauge models, with topologically trivial target space and vacuum manifold. They are prototypes for possible analogous…
In this article we introduce a definition of topological minimal sets, which is a generalization of that of Mumford-Shah-minimal sets. We prove some general properties as well as two existence theorems for topological minimal sets. As an…
Two (strongly) zero-dimensional Lindel\"of topological groups whose product has positive covering dimension are constructed. An example of a Lindel\"of (strongly) zero-dimensional space whose free and free Abelian topological groups are not…
We investigate the interface coupling between the 2D sine-Gordon equation and the 2D wave equation in the context of a Josephson window junction using a finite volume numerical method and soliton perturbation theory. The geometry of the…
A contractive $n$-tuple $A=(A_1,...,A_n)$ has a minimal joint isometric dilation $S=(S_1,...,S_n)$ where the $S_i$'s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When $A$…
We prove the existence of nonperiodic, properly embedded minimal surfaces in $\mathbb{R}^2\times\mathbb{S}^1$ with genus zero, infinitely many ends and one limit end (in particular, they have infinite total curvature).
We give a simple construction of new, complete, finite volume manifolds $M$ of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetric ends of different ranks and their fundamental groups are…
We construct a lattice model of compact (2+1)-dimensional Maxwell-Chern- Simons theory, starting from its formulation in terms of gauge invariant quantities proposed by Deser and Jackiw. We thereby identify the topological excitations and…
We exhibit many examples of closed symplectic manifolds on which there is an autonomous Hamiltonian whose associated flow has no nonconstant periodic orbits (the only previous explicit example in the literature was the torus T^2n (n\geq 2)…
A longstanding open problem asks for an aperiodic monotile, also known as an "einstein": a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
The space-like hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this space-like hypersurface would imply that the apparently observable universe (the sphere of…
A new type of three-dimensional magnetic soliton in easy-axis ferromagnets is predicted by taking simultaneous account of the Dzyaloshinsky-Moriya interaction and an external magnetic field. The numerically obtained static three-dimensional…
Strongly zero-dimensional topological groups $G_1$, $G_2$, and $G$ such that $G_1\times G_2$ has positive covering dimension and $G$ contains a closed subgroup of positive covering dimension are constructed. Moreover, all finite powers of…
A family of modified Nicole models is introduced. We show that for particular members of the family a topological soliton with a non-trivial value of the Hopf index exists. The form of the solitons as well as their energy and topological…
Certain static soliton configurations of gauge fields in 4+1 dimensions correspond to the instanton in 4-Euclidean dimensions ``turned on its side,'' becoming a monopole in 4+1. The periodic instanton solution can be used with the method of…
The representation in terms of Ernst's complex potential is used to describe and analyze dilaton-axion theories with potential. The set of such systems is divided into pairs of dual systems with respect to the inversion of the Ernst…