Related papers: Localized modes in mini-gaps opened by periodicall…
We model the nonlinear behaviour of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or anti-ferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional…
We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in…
In this paper we consider a 2D hexagonal crystal lattice model first proposed by Marin, Eilbeck and Russell in 1998. We perform a detailed numerical study of nonlinear propagating localized modes, that is, propagating discrete breathers and…
We discuss the process by which energy, initially evenly distributed in a nonlinear lattice, can localize itself into large amplitude excitations. We show that, the standard modulational instability mechanism, which can initiate the process…
We introduce a model of one- and two-dimensional (1D and 2D) optical media with the $\chi ^{(2)}$ nonlinearity whose local strength is subject to cusp-shaped spatial modulation, $\chi ^{(2)}\sim r^{-\alpha }$, with $\alpha >0$, which can be…
Solitons are studied in a model of a fiber Bragg grating (BG) whose local reflectivity is subjected to periodic modulation. The superlattice opens an infinite number of new bandgaps in the model's spectrum. Averaging and numerical…
We study numerically interaction of spatially localized modes in strongly scattering two-dimensional media. We move eigenvalues in the complex plane by changing gradually the index of a single scatterer. When spatial and spectral overlap is…
We introduce a two-component one-dimensional system, which is based on two nonlinear Schr\"{o}dinger/Gross-Pitaevskii equations (GPEs) with spatially periodic modulation of linear coupling ("Rabi lattice") and self-repulsive nonlinearity.…
We study the dynamics of discrete breathers -- spatially localized and time-periodic solutions -- inside the bandgap of a nonlinear honeycomb lattice where the dispersion landscape approaches a so-called semi-Dirac point in which the bands…
We report on the experimental generation of discrete breather states (intrinsic localized modes) in frustrated Josephson arrays. Our experiments indicate the formation of discrete breathers during the transition from the static to the…
We study the structure and stability of discrete breathers (both pinned and mobile) in two-dimensional nonlinear anisotropic Schrodinger lattices. Starting from a set of identical one-dimensional systems we develop the continuation of the…
We study the existence and stability of solitons in the quadratic nonlinear media with spatially localized ${\cal PT}$-symmetric modulation of the linear refractive index. Families of stable one and two hump solitons are found. The…
We prove the most general theorem about spectral stability of multi-site breathers in the discrete Klein-Gordon equation with a small coupling constant. In the anti-continuum limit, multi-site breathers represent excited oscillations at…
We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schr\"{o}dinger (DNLS) equation, including a local linear or nonlinear defect. Discrete solitons pinned to the…
We study localized modes (LMs) of the one-dimensional Gross-Pitaevskii/nonlinear Schr\"{o}dinger equation with a harmonic-oscillator (parabolic) confining potential, and a periodically modulated coefficient in front of the cubic term…
It is found that localized solitons in the strongly coupled cigar shaped Bose-Einstein condensate form two distinct classes. The one without a background is an asymptotically vanishing, localized soliton, having a wave-number, which has a…
We consider the localized modes (bright solitons) described by one-dimensional quintic nonlinear Schrodinger equation with a periodic potential. In the case of attractive nonlinearity we deduce sufficient conditions for collapse. We show…
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,…
We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by pair-transition coupled two-component Bose-Einstein condensate. We demonstrate the interference effects can induce several…
We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including…