Related papers: Geometric solitons with vortex structures for some…
We study the soliton flow on the domain of a twistorial harmonic morphism between Riemannian manifolds of dimensions four and three. Assuming real-analyticity, we prove that, for the Gibbons-Hawking construction, any soliton flow is…
Topological wave structures, such as vortices and skyrmions, appear in a variety of quantum and classical wave fields, including optics and acoustics. In particular, optical vortices have found numerous applications ranging from quantum…
We derive equations of motion for topological solitons in antiferromagnets under the combined action of perturbations such as an external magnetic field and torque-generating electrical current. Aside from conservative forces, such…
Certain hyperbolic monopoles and all hyperbolic vortices can be constructed from SO(2) and SO(3) invariant Euclidean instantons, respectively. This observation allows us to describe a large class of hyperbolic monopoles as hyperbolic…
The problem of vortex pair motion in two-dimensional plane radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases…
We introduce multi-soliton sets in the two-dimensional medium with the second-harmonic-generating nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are…
We discuss the general properties of periodic vortex arrangements in rotating superfluids. The different possible structures are classified according to the symmetry space-groups and the circulation number. We calculate numerically several…
Models are developed for the motion of charge-2 Abelian Higgs vortices through the 2-vortex moduli space $M$, with the vortices excited by their shape mode oscillations. The models simplify to the well-known geodesic flow on $M$, modified…
A superconducting rod with a magnetic moment on top develops vortices obtained here through 3D calculations of the Ginzburg-Landau theory. The inhomogeneity of the applied field brings new properties to the vortex patterns that vary…
Formation and evolution of topological defects in course of non-equilibrium symmetry breaking phase transitions is of wide interest in many areas of physics, from cosmology through condensed matter to low temperature physics. Its study in…
In the present article we obtain classification results and topological obstructions for the existence of translating solitons of the mean curvature flow.
The response of superfluids to the external rotation, evidenced by emergence of quantised vortices, distinguishes them from conventional fluids. In this work, we demonstrate that the number of vortices in a stirred polariton condensate…
We deal with solitons of the mean curvature flow. The definition of \textit{translating solitons on a light-like direction} in Minkowski 3-space is introduced. Firstly, we classify those which are graphical, \textit{translation surfaces},…
It is shown that stationary vortex structures can be excited in a ferrite film. This is the first proposal for creating vortex structures in the important cm and mm wavelength ranges. It is shown that both linear and nonlinear structures…
The motion of a neutron superfluid condensate in a pulsar is studied. Several theorems of general-relativistic hydrodynamics are proved for a superfluid. The average density distribution of vortex lines in pulsars and their…
Vortices are localized planar structures that attain topological stability and can be used to describe collective behavior in a diversity of situations of current interest in nonlinear science. In high energy physics, vortices engender…
In this paper we introduce and study a new kind of hyperbolic geometric flows --dissipative hyperbolic geometric flow. This kind of flow is defined by a system of quasilinear wave equations with dissipative terms. Some interesting exact…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
We focus on BPS solutions of the gauged O(3) Sigma model, due to Schroers, and use these ideas to study the geometry of the moduli space. The model has an asymmetry parameter $\tau$ breaking the symmetry of vortices and antivortices on the…
Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements.…