相关论文: Discrete solitons and vortices in hexagonal and ho…

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.…

In this paper, we study the discrete cubic nonlinear Schroedinger lattice under Hamiltonian perturbations. First we develop a complete isospectral theory relevant to the hyperbolic structures of the lattice without perturbations. In…

We address the existence, stability, and dynamics of single-ring and multi-ring vorticity-carrying necklace solitons under the action of the Kerr nonlinearity and a Bessel-lattice potential modulated in the azimuthal direction. The model…

In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them with those in lattices with the cubic nonlinearity. This comparison has become especially relevant in light of recent…

We show for the first time that highly localized in-plane breathers can propagate in specific directions with minimal lateral spreading in a model 2-D hexagonal non-linear lattice. The lattice is subject to an on-site potential in addition…

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…

It is well known that the two-dimensional (2D) nonlinear Schr\"odinger equation (NLSE) with the cubic-quintic (CQ) nonlinearity supports a family of stable fundamental solitons, as well as solitary vortices (alias vortex rings), which are…

We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying…

We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion and the $6-$fold orientational order…

Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…

We analytically study stability of sliding lattice of Josephson vortices driven by a transport current in the stack direction in strong in-plane magnetic field. In contrast to recent findings we obtain that there are no diverse…

We address the issue of nonlinear modes in a two-dimensional waveguide array, spatially distributed in the Lieb lattice geometry, and modeled by a saturable nonlinear Schr\"odinger equation. In particular, we analyze the existence and…

We address the existence and stability of two-dimensional solitons in optical or matter-wave media, which are supported by purely nonlinear lattices in the form of a periodic array of cylinders with self-focusing nonlinearity, embedded into…

We consider a parametrically driven damped discrete nonlinear Schr\"odinger (PDDNLS) equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental discrete bright solitons. We show…

We show that double-charge discrete optical vortices may be completely stable in hexagonal photonic lattices where single-charge vortices always exhibit dynamical instabilities. Even when unstable the double-charge vortices typically have a…

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 report on the existence and stability of multidimensional bound solitonic states in harmonically-trapped scalar Bose-Einstein condensates. Their equilibrium separation, as a measure of the strength of the soliton-soliton or the solitonic…

In the present work, we numerically explore the existence and stability properties of different types of configurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings,…

We revisit the theme of non-nearest-neighbor interactions in nonlinear dynamical lattices, in the prototypical setting of the discrete nonlinear Schrodinger equation. Our approach offers a systematic way of analyzing the existence and…

We obtain sharp criteria for transverse stability and instability of line solitons in the discrete nonlinear Schr\"{o}dinger equations on one- and two-dimensional lattices near the anti-continuum limit. On a two-dimensional lattice, the…