Related papers: Discrete-symmetry vortices as angular Bloch modes
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…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
We study the effect of lifting the degeneracy of vortex modes with a PT symmetric defect, using discrete vortices in a circular array of nonlinear waveguides as an example. When the defect is introduced, the degenerate linear vortex modes…
I show the existence of a new type of vortex solution which is non-static but stationary and carries angular momentum. This {\it spinning vortex} can be embedded in models with trivial vacuum topology like a model with $SU(2)_{global}\times…
In this paper, we consider the dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schroedinger model, a model of interest both to atomic physics and to nonlinear optics. We find that in a way…
Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition…
We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices, and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance…
The fundamental mode of rotation in quantum fluids is given by a vortex, whose quantized value yields the orbital angular momentum (OAM) per particle. If the vortex is displaced (off-centered) from the reference point for rotation, the…
Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…
The connection between symmetries and conservation laws is a cornerstone of physics. It underlies Bloch's theorem which explains wave phenomena in all linear periodic systems. Here we demonstrate that, in a nonlinear grating with memory,…
We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear…
Densely arranged optical vortices are natural solutions of high-symmetry Bloch modes in photonic crystals. However, strict symmetry constraints limit the potential spatial configurations of nearfield vortices, restricting the control over…
We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…
Our understanding of the mechanism by which topological defects are formed in symmetry breaking phase transitions has recently changed. We examine the non-equilibrium dynamics of defect formation for weakly-coupled global O(N) theories…
We study generic waves without rotational symmetry in (2+1) - dimensional noncommutative scalar field theory. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by…
We study discrete vortices in the anti-continuum limit of the discrete two-dimensional nonlinear Schr{\"o}dinger (NLS) equations. The discrete vortices in the anti-continuum limit represent a finite set of excited nodes on a closed discrete…
We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schr\"odinger equation. We show that these solutions present a central phase singularity whose charge is restricted by…
It is known that, in continuous media, composite solitons with hidden vorticity, which are built of two mutually symmetric vortical components whose total angular momentum is zero, may be stable while their counterparts with explicit…
Quantized vortices are the prototypical feature of superfluidity. Pervasive in all natural systems, vortices are yet to be observed in dipolar quantum gases. Here, we exploit the anisotropic nature of the dipole-dipole interaction of a…
We consider effects of anisotropy on solitons of various types in two-dimensional nonlinear lattices, using the discrete nonlinear Schr{\"{o}}dinger equation as a paradigm model. For fundamental solitons, we develop a variational…