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We introduce a system of two linearly coupled discrete nonlinear Schr\"{o}dinger equations (DNLSEs), with the coupling constant subject to a rapid temporal modulation. The model can be realized in bimodal Bose-Einstein condensates (BEC).…
We address the properties of two-dimensional surface solitons supported by the interface of a waveguide array whose nonlinearity is periodically modulated. When the nonlinearity strength reaches its minima at the points where the linear…
Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were…
This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…
The (1+1)-dimensional gauge model of two complex self-interacting scalar fields that interact with each other through an Abelian gauge field and a quartic scalar interaction is considered. It is shown that the model has nontopological…
We study collisions of moving nonlinear-Schr\"{o}dinger solitons with a $\mathcal{PT}$-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and,…
A model of the optical media with a spatially structured Kerr nonlinearity is introduced. The nonlinearity strength is modulated by a set of singular peaks on top of a self-focusing or defocusing uniform background. The peaks may include a…
We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and…
I study vector solitons involving two incoherently-coupled field components in periodic PT-symmetric optical lattices. The specific symmetry of the lattice imposes the restrictions on the symmetry of available vector soliton states. While…
A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all…
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…
Parity-time(PT) symmetric lattices have been widely studied in controlling the flow of waves, and recently moir\'e superlattices, connecting the periodic and non-periodic potentials, are introduced for exploring unconventional physical…
In various supersymmetric extensions of the Standard Model there appear non-topological solitons due to the existence of U(1) global symmetries associated with Baryon and/or Lepton quantum numbers. Trilinear couplings (A-terms) in the…
We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BEC). The soliton solutions to the mean-field equations are obtained…
We introduce a two-dimensional (2D) system, which can be implemented in dual-core planar optical couplers with the Kerr nonlinearity in its cores, making it possible to blend effects of the PT symmetry, represented by the balanced linear…
We consider one-dimensional solitons in a binary Bose-Einstein condensate with linear coupling between the components, trapped in an optical-lattice potential. The inter-species and intra-species interactions may be both repulsive or…
We derive the nonlinear equations governing the dynamics of three-dimensional (3D) disturbances in a nonuniform rotating self-gravitating fluid under the assumption that the characteristic frequencies of disturbances are small compared to…
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 existence and stability of localized states in the discrete nonlinear Schr{\"o}dinger equation (DNLS) on two-dimensional non-square lattices. The model includes both the nearest-neighbor and long-range interactions. For the…
We investigate the existence and linear stability of solitons in the nonlinear Schr\"odinger lattices in the strong coupling regime. Focusing and defocusing nonlinearities are considered, giving rise to bright and dark solitons. In this…