Related papers: Solitons in composite linear-nonlinear moir\'{e} l…
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…
Phase frustration in periodic lattices is responsible for the formation of dispersionless flat bands. The absence of any kinetic energy scale makes flat band physics critically sensitive to perturbations and interactions. We report here on…
The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation with a periodic potential is demonstrated by means of the variational approximation (VA)…
Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice…
We show that surface solitons form continuous families in one-dimensional complex optical potentials of a certain shape. This result is illustrated by non-Hermitian gap-surface solitons at the interface between a uniform conservative medium…
We consider the three-dimensional (3D) mean-field model for the Bose-Einstein condensate (BEC), with a 1D nonlinear lattice (NL), which periodically changes the sign of the nonlinearity along the axial direction, and the harmonic-oscillator…
We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schrodinger equation with a sinusoidal potential, such as photonic crystals, waveguide arrays,…
In the present work, we revisit a recently proposed and experimentally realized topological 2D lattice with periodically time-dependent interactions. We identify the fundamental solitons, previously observed in experiments and direct…
The phase diagram of binary mixtures of particles interacting via a pair potential of parallel dipoles is computed at zero temperature as a function of composition and the ratio of their magnetic susceptibilities. Using lattice sums, a rich…
The O(3) sigma model in two spatial dimensions admits topological (Bogomol'nyi) lower bound on its energy. This paper proposes a lattice version of this system which maintains the Bogomol'nyi bound and allows the explicit construction of…
We consider an array of double oligomers in an optical waveguide device. A mathematical model for the system is the coupled discrete nonlinear Schr\"odinger (NLS) equations, where the gain-and-loss parameter contributes to the…
We predict that photonic moir\'e patterns created by two mutually twisted periodic sublattices in quadratic nonlinear media allow the formation of parametric solitons under conditions that are strongly impacted by the geometry of the…
We consider a PT-symmetric ladder-shaped optical array consisting of a chain of waveguides with gain coupled to a parallel chain of waveguides with loss. All waveguides have the focusing Kerr nonlinearity. The array supports two co-existing…
We report the existence of stable symmetric vortex-type solutions for two-dimensional nonlinear discrete dissipative systems governed by a cubic-quintic complex Ginzburg-Landau equation. We construct a whole family of vortex solitons with a…
We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~$2$ of lattices. %as considered in \cite{Ma1} and \cite{Ma2}. We also consider some related…
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…
A modification of the usual Type-II second-harmonic-generation model is proposed, which includes two additional features: linear conversion and walkoff (group-velocity difference) between two components of the fundamental-frequency (FF)…
We report localized and unidirectional nonlinear traveling edge waves discovered theoretically and numerically in a 2D mechanical (phononic) topological insulator. The lattice consists of a collection of pendula with weak Duffing…
We study stability and dynamics of the single cylindrically symmetric solitary structures and dipolar solitonic molecules in spatially nonlocal media. The main properties of the solitons, vortex solitons, and dipolar solitons are…
In this report, fundamental educational concepts of linear and non-linear equations and solutions of nonlinear equations from the book High-Temperature Superconductivity: The Nonlinear Mechanism and Tunneling Measurements (Kluwer Academic…