Related papers: Three-dimensional static vortex solitons in incomm…
We clarify relations among topological solitons in various dimensions: a domain wall, non-Abelian vortex, magnetic monopole and Yang-Mills instanton, together with a (non-Abelian) sine-Gordon soliton, baby Skyrmion (lump) and Skyrmion. We…
In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; there exist stable…
We study solitons in a zig-zag lattice of magnetic dipoles. The lattice comprises two sublattices of parallel chains with magnetic dipoles at their vertices. Due to orthogonal easy planes of rotation for dipoles belonging to different…
Topological magnetic structures, such as Hopfions, are central to three-dimensional magnetism, but their characterization in complex geometries remains challenging. We introduce a robust finite-element method for calculating the Hopf index…
An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in…
We show the existence of stable two- and three-dimensional vortex solitons carrying multiple, spatially separated, single-charge topological dislocations nested around a vortex-ring core. Such new nonlinear states are supported by…
This Letter deals with topological solitons in an O(3) sigma model in three space dimensions (with a Skyrme term to stabilize their size). The solitons are classified topologically by their Hopf number N. The N=2 sector is studied; in…
We study formation of rotating three-dimensional high-order solitons (azimuthons) in Bose Einstein condensate with attractive nonlocal nonlinear interaction. In particular, we demonstrate formation of toroidal rotating solitons and…
Motivated by recent experiments\cite{BA}\cite{BB}, we study quasi 2D ferromagnetic condensates with various aspect ratios. We find that in zero magnetic field, dipolar energy generates a local energy minimum with all the spins lie in the 2D…
We elaborate a mechanism for the formation of stable solitons of the semi-vortex type (with vorticities 0 and 1 in their two components), populating a finite bandgap in the spectrum of the spin-orbit-coupled binary Bose-Einstein condensate…
Vortex-antivortex pairs in 2D easy-plane ferromagnets have characteristics of solitons in two dimensions. We investigate numerically and analytically the dynamics of such vortex pairs. In particular we simulate numerically the head-on…
The magnetization in a magnetic microdot made from soft magnetic materials can have a vortex-like ground state structure resulting from competition between the exchange and dipolar interactions. Normal mode magnon frequencies for such dots…
In this talk I study the topology of mathematically idealised center vortices, defined in a gauge invariant way as closed (infinitely thin) flux surfaces (in D=4 dimensions) which contribute the $n^{th}$ power of a non-trivial center…
A gravity dual of a superconductor at finite temperature has been recently proposed. We present the vortex configuration of this model and study its properties. In particular, we calculate the free energy as a function of an external…
We introduce a dynamical model of a Bose-Einstein condensate based on the 2D Gross-Pitaevskii equation, in which the nonlinear coefficient is a function of radius. The model describes a situation with spatial modulation of the negative…
Cubic chiral magnets exhibit a remarkable diversity of two-dimensional topological magnetic textures, including skyrmions. However, the experimental confirmation of topological states localized in all three spatial dimensions remains…
Vortices are among the simplest topological structures, and occur whenever a flow field `whirls' around a one-dimensional core. They are ubiquitous to many branches of physics, from fluid dynamics to superconductivity and superfluidity, and…
A non-relativistic scalar field coupled minimally to electromagnetism supports in the presence of a homogeneous background electric charge density the existence of smooth, finite-energy topologically stable flux vortices. The static…
We show that transmutation of linear momentum into position may occur in a system of three magnetic vortices thanks to a direct link between topology and dynamics in a ferromagnet. This happens via exchange between the linear momentum of a…
We present a detailed numerical study of solutions to the Zakharov-Kuznetsov equation in three spatial dimensions. The equation is a three-dimensional generalization of the Korteweg-de Vries equation, though, not completely integrable. This…