Related papers: Two-dimensional solitons at interfaces between bin…

Solitons in the fractional space, supported by lattice potentials, have recently attracted much interest. We consider the limit of deep one- and two-dimensional (1D and 2D) lattices in this system, featuring finite bandgaps separated by…

We predict the existence of spatial-spectral vortex solitons in one-dimensional periodic waveguide arrays with quadratic nonlinear response. In such vortices the energy flow forms a closed loop through the simultaneous effects of phase…

We study two-dimensional (2D) solitons in the mean-field models of ultracold gases with long-range quadrupole-quadrupole interaction (QQI) between particles. The condensate is loaded into a deep optical-lattice (OL) potential, therefore the…

We study experimentally light localization at phase-slip waveguides and at the intersection of phase-slips in a two-dimensional (2D) square photonic lattice. Such system allows to observe a variety of effects, including the existence of…

We study light propagation in waveguide arrays made in Kerr nonlinear media with a transverse refractive index gradient, and we find that the presence of the refractive index gradient leads to the appearance of a number of new soliton…

Two-dimensional (2D) equations describing the nonlinear interaction between upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal nonlinearity in the equations results in the possibility of existence of stable 2D nonlinear…

We discuss the formation of self-trapped localized states near the edge of a semi-infinite array of nonlinear waveguides. We study a crossover from nonlinear surface states to discrete solitons by analyzing the families of odd and even…

We consider an array of straight nonlinear waveguides constituting a two-dimensional square lattice, with a few central layers tilted with respect to the rest of the structure. It is shown that such configuration represents a line defect,…

We consider a dipolar Bose-Einstein condensate trapped in an array of two-well systems with an arbitrary orientations of the dipoles relative to the system's axis. The system can be built as a chain of local traps sliced into two parallel…

Resonant mode interactions in weakly nonlinear multi-dimensional lattices and related effects are described. We concentrate on formal description of the phenomenon and consider as examples mode interactions and evolution equations for…

Two-dimensional (2D) perovskite oxide interfaces are ideal systems where diverse emergent properties can be uncovered.The formation and modification of polaronic properties due to short-range strong charge-lattice interactions of 2D…

In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one components, namely interlaced solitons. These are waveforms in which in the relevant anti-continuum limit, i.e.…

We report on the existence and stability of multicolor lattice vortex solitons constituted by coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic nonlinear media. It is shown that the solitons are stable…

We analytically study plasma solitary waves, or solitons, in a two-dimensional (2D) electron system (ES) placed in close proximity to and between two ideal metallic gates. As a rule, solitons are described using a perturbative approach…

We report results of a systematic analysis of spatial solitons in the model of 1D photonic crystals, built as a periodic lattice of waveguiding channels, of width D, separated by empty channels of width L-D. The system is characterized by…

We obtain analytical expressions for an effective potential of interaction between two- and three-dimensional (2D and 3D) solitons (including the case of 2D vortex solitons) belonging to two different modes which are incoherently coupled by…

This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of…

We study experimentally the interaction of a soliton with a nonlinear lattice. We observe the formation of a novel type of composite soliton created by strong coupling of mutually incoherent periodic and localized beam components. By…

Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical…

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…