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A general approach allowing to find the analytical expressions for equilibrium magnetic structures in small and flat magnetic nano-sized cylinders of arbitrary shape made of soft magnetic material is presented. The resulting magnetization…
We address the evolution of higher-order excited states, such as vortex and multi-hump solitons, in nonlocal media with synthetic, competing focusing and defocusing nonlinearities with different nonlocal transverse scales. We reveal that…
We introduce a model of one- and two-dimensional (1D and 2D) optical media with the $\chi ^{(2)}$ nonlinearity whose local strength is subject to cusp-shaped spatial modulation, $\chi ^{(2)}\sim r^{-\alpha }$, with $\alpha >0$, which can be…
This article presents an overview of experimental efforts in recent years related to multidimensional solitons in Bose-Einstein condensates. We discuss the techniques used to generate and observe multidimensional nonlinear waves in…
A study of high-order solitons in three nonlocal nonlinear Schr\"{o}dinger equations is presented, which includes the \PT-symmetric, reverse-time, and reverse-space-time nonlocal nonlinear Schr\"{o}dinger equations. General high-order…
We establish existence and stabilty results for solitons in noncommutative scalar field theories in even space dimension $2d$. In particular, for any finite rank spectral projection $P$ of the number operator ${\mathcal N}$ of the…
By using ZEUS cluster at Embry-Riddle Aeronautical University we perform extensive numerical simulations based on a two-dimensional Fourier spectral method Fourier spatial discretization and an explicit scheme for time differencing) to find…
We introduce a two-dimensional (2D) discrete nonlinear Schr\"{o}dinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong…
By methods of numerical simulations the dynamics of interaction of radially symmetric Bellavin-Polyakov type topological vortex in (2+1)-dimensional O(3) nonlinear sigma model is investigated. Obtained numerically the model of topological…
Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have…
We report analytical solutions for spatial solitons supported by layers of a quadratically nonlinear material embedded into a linear planar waveguide. A full set of symmetric, asymmetric, and antisymmetric modes pinned to a symmetric pair…
We investigate the soliton structure of novel (2+1)-dimensional nonlinear partial differential evolution(NLPDE) equations which may govern the behavior of a barothropic relaxing medium beneath high-frequency perturbations. As a result, we…
We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly…
Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a five-fold…
Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity…
Solitons, nonlinear particle-like excitations with inalterable properties (amplitude, shape, and velocity) as they propagate, are omnipresent in many branches of science---and in physics in particular. Flat-top solitons are a novel type of…
We introduce a 2D network built of $\mathcal{PT}$-symmetric dimers with on-site cubic nonlinearity, the gain and loss elements of the dimers being linked by parallel square-shaped lattices. The system may be realized as a set of…
We study localized two- and three-dimensional Langmuir solitons in the framework of model based on generalized nonlinear Schr\"odinger equation that accounts for local and nonlocal contributions to electron-electron nonlinearity. General…
We show, by means of numerical and analytical methods, that media with a repulsive nonlinearity which grows from the center to the periphery support a remarkable variety of previously unknown complex stationary and dynamical…
We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the…