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Here we revisit the topic of stationary and propagating solitonic excitations in self-repulsive three-dimensional Bose-Einstein condensates by quantitatively comparing theoretical analysis and associated numerical computations with our…
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…
We study the problem of constructing bulk and surface embedded modes (EMs) inside the quasi-continuum band of a square lattice, using a potential engineering approach \`a la Wigner and von Neumann. Building on previous results for the…
We report solutions for stable compound solitons in a three-dimensional quasi-phase-matched photonic crystal with the quadratic ($\chi ^{(2)}$) nonlinearity. The photonic crystal is introduced with a checkerboard structure, which can be…
We have performed numerical analysis of the two-dimensional (2D) soliton solutions in Bose-Einstein condensates with nonlocal dipole-dipole interactions. For the modified 2D Gross-Pitaevski equation with nonlocal and attractive local terms,…
In this work, we focus our studies on the subject of nonlinear discrete self-trapping of S=2 (doubly-charged) vortices in two-dimensional photonic lattices, including theoretical analysis, numerical computation and experimental…
Solitons are non-dispersing localized waves that occur in diverse physical settings. A variety of optical solitons have been observed, but versions that involve both spatial and temporal degrees of freedom are rare. Optical fibers designed…
We introduce a model for spatiotemporal modelocking in multimode fiber lasers, which is based on the (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation (cGLE) with conservative and dissipative nonlinearities and a…
We study the stability and structure of vortices emerging in two-dimensional quantum dots in high magnetic fields. Our results obtained with exact diagonalization and density-functional calculations show that vortex structures can be found…
We construct a variety of novel localized states with distinct topological structures in the 3D discrete nonlinear Schr{\"{o}}dinger equation. The states can be created in Bose-Einstein condensates trapped in strong optical lattices, and…
Various families of charge-one vortex solitons in two-dimensional periodic media are reported. These vortices reside either in the semi-infinite gap or higher band gaps of the media. For both Kerr and saturable nonlinearities (either…
This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history. Some findings, such as optical solitons supported by thermal nonlinearity, and by the orientational nonlinearity…
We produce families of two-dimensional gap solitons (GSs) maintained by moir\'{e} lattices (MLs) composed of linear and nonlinear sublattices, with the defocusing sign of the nonlinearity. Depending on the angle between the sublattices, the…
We study two-dimensional fundamental and vortex solitons in polariton condensates with spin-orbit coupling and Zeeman splitting evolving in square arrays of microcavity pillars. Due to repulsive excitonic nonlinearity such states are…
The existence and stability of defect solitons supported by parity-time (PT) symmetric superlattices with nonlocal nonlinearity are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive or zero…
We predict the existence and address the stability of two-dimensional surface solitons featuring topologically complex shapes, including dipoles, vortices, and bound states of vortex solitons, at the interface of nonlocal thermal media.…
We consider soliton dynamics and stability in a nonlinear lattice formed by alternating domains with focusing cubic and saturable nonlinearities. We find that in such lattices solitons centered on cubic domains may be stabilized even in…
Using the variational approximation and numerical simulations, we study one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an optical-lattice potential. We consider the case of inter-species repulsion, while the…
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions:…
We analyze nonlinear collective effects near surfaces of semi-infinite periodic systems with multi-gap transmission spectra and introduce a novel concept of multi-gap surface solitons as mutually trapped surface states with the components…