Stabilizing vortex solitons with high values of the topological charge, S, is a challenging issue in optics, studies of Bose-Einstein condensates (BECs) and other fields. To develop a new approach to the solution of this problem, we consider a two-dimensional dipolar BEC under the action of an axisymmetric radially periodic lattice potential, V (r) ∼ cos(2r + δ), with dipole moments polarized perpendicular to the system's plane, which gives rise to isotropic repulsive dipole-dipole interactions (DDIs). Two radial lattices are considered, with δ = 0 and π, i.e., a potential maximum or minimum at r = 0, respectively. Families of vortex gap soliton (GSs) with S = 1 and S ≥ 2, the latter ones often being unstable in other settings, are completely stable in the present system (at least, up to S = 11), being trapped in different annular troughs of the radial potential. The vortex solitons with different S may stably coexist in sufficiently far separated troughs. Fundamental GSs, with S = 0, are found too. In the case of δ = 0, the fundamental solitons are ring-shaped modes, with a local minimum at r = 0.At δ = π, they place a density peak at the center.

We study the spatiotemporal solitary modes that propagate in a hollow twisted cylinder waveguide pipe with a self-focusing Kerr nonlinearity. Three generic solitary modes, one belonging to the zero-harmonic (0H) and the other two belonging to the first-harmonic (1H), are found in the first rotational Brillouin zone. The 0H solitary modes can be termed as a quasi-1D (one-dimensional) temporal soliton. Their characteristics depend only on the energy flow. The 1H solitary mode can be termed a quasi-2D (two-dimensional) bullet, whose width is much narrower than the angular domain of the waveguide. In contrast to the 0H mode, the characteristics of the 1H solitary mode depend on both their energy flow and the rotating speed of the waveguide. We demonstrate numerically that the 1H solitary modes are stable when their energy flow is smaller than the threshold norm of the Townes soliton. The boundaries of the bistable area for these two types of solitary modes are predicted by the analyses via two-mode approximation. This prediction is in accordance with the numerical findings. We also demonstrate analytically that the 1H solitary mode of this system can be applied to emulate the nonlinear dynamics of solitary modes with 1D Rashba spin-orbit (SO) coupling by optics. Two degenerated states of the 1H solitary mode, semi-dipole and mixed mode, are found from this setting via the mechanism of SO coupling. Collisions between the pair of these two types of solitary modes are also discussed in the paper. The pair of the 0H solitary mode features only the elastic collision, whereas the pair of 1H solitary modes can feature both elastic and inelastic collision when the total energy flow of the two modes are smaller or close to the threshold norm of the Townes soliton. * Electronic address: