Related papers: Geometric solitons with vortex structures for some…
Several geometric flows on symplectic manifolds are introduced which are potentially of interest in symplectic geometry and topology. They are motivated by the Type IIA flow and T-duality between flows in symplectic geometry and flows in…
The theory of the vortex filament in three-dimensional fluid dynamics, consisting mainly of the models up to the third-order approximation, is an attractive subject in both physics and mathematics. Many efforts have been devoted to the…
As is well-known, two-dimensional and three-dimensional superfluids under rotation can support topological excitations such as quantized point vortices and line vortices respectively. Recently, we have studied how, in a hypothetical…
The formation of zonal flows and vortices in the generalized Charney-Hasegawa-Mima equation is studied. We focus on the regime when the size of structures is comparable to or larger than the deformation (Rossby) radius. Numerical…
We construct a type-II holographic superconductor from an anisotropic rotating background metric. We study the effects of the magnetic field on the vortex structure, including continuous deformations both from triangular to square lattices…
At Bradlow's limit, the moduli space of Bogomol'nyi vortices on a compact Riemann surface of genus $g$ is determined. The K\"{a}hler form, and the volume of the moduli space is then computed. These results are compared with the…
Atomic or molecular bosons in harmonically confined optical lattices exhibit a wedding cake structure consisting of insulating (Mott) shells. It is shown that superfluid regions emerge between Mott shells as a result of fluctuations due to…
We give a survey of the following six closely related topics: (i) a general method for constructing a soliton hierarchy from a splitting of a loop algebra into positive and negative subalgebras, together with a sequence of commuting…
When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological…
We analyse the topological (knot-theoretic) features of a certain codimension-one bifurcation of a partially hyperbolic fixed point in a flow on $\real^3$ originally described by Shil'nikov. By modifying how the invariant manifolds wrap…
We discover the existence of vortex solitons supported by the surface between two optical lattices imprinted in Kerr-type nonlinear media. Such solitons can feature strongly noncanonical profiles, and we found that their properties are…
It is known that the Schr\"odinger flow on a complex Grassmann manifold is equivalent to the matrix non-linear Schr\"odinger equation and the Ferapontov flow on a principal Adjoint U(n)-orbit is equivalent to the $n$-wave equation. In this…
We introduce discrete multivortex solitons in a ring of nonlinear oscillators coupled to a central site. Regular clusters of discrete vortices appear as a result of mode collisions and we show that their stability is determined by global…
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…
In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…
We report stable composite vortex solitons in the model of a three-dimensional photonic crystal with the third-harmonic (TH) generation provided by the quasi-phase-matched quadratic nonlinearity. The photonic crystal is designed with a…
We construct the vortex Floer homology group $VHF (M,\mu;H)$ for an aspherical Hamiltonian $G$-manifold $(M, \omega)$ with moment map $\mu$ and a class of $G$-invariant Hamiltonian loop $H_t$, following the proposal of [3]. This is a…
The kinetic part of the Rasetti-Regge action I_{RR} for vortex lines is studied and links to string theory are made. It is shown that both I_{RR} and the Polyakov string action I_{Pol} can be constructed with the same field X^mu. Unlike…
We report an observation of a stable soliton-like structure on the surface of a ferrofluid, generated by a local perturbation in the hysteretic regime of the Rosensweig instability. Unlike other pattern-forming systems with localized 2D…
Vorticity is a key ingredient to a broad variety of fluid phenomena, and its quantised version is considered to be the hallmark of superfluidity. Circulating flows that correspond to vortices of a large topological charge, termed giant…