Existence of localized modes supported by the PT-symmetric nonlinear lattices is reported. The system considered reveals unusual properties: unlike other typical dissipative systems it possesses families (branches) solutions, which can be parametrized propagation constant; relatively narrow appear to stable, even when conservative lattice potential absent; finally, supports stable multipole solutions.

We consider, by means of the variational approximation (VA) and direct numerical simulations Gross-Pitaevskii (GP) equation, dynamics 2D 3D condensates with a scattering length containing constant harmonically varying parts, which can be achieved an ac magnetic field tuned to Feshbach resonance. For rapid time modulation, we develop approach based on averaging GP equation,without using VA. In case, both VA simulations, as well method, reveal existence stable self-confined without external...

The dynamics of localized excitations in an array Bose-Einstein condensates (BECs) is investigated the framework nonlinear lattice theory. existence temporarily stable ground states displaying atomic population distribution on very few sites (intrinsic modes), as well distributions involving many (envelope solitons), studied both numerically and analytically. origin properties these modes are shown to be inherently connected with interplay between macroscopic quantum tunneling...

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss validity criterion for suggested Vakhitov Kolokolov. The maximum chirp (initial focusing defocusing cloud) that can lead stable to collapse even before number atoms reaches its critical limit is obtained several specific cases....

Recent experimental and theoretical advances in the creation description of bright matter wave solitons are reviewed. Several aspects taken into account, including physics soliton train formation as nonlinear Fresnel diffraction, soliton-soliton interactions, propagation presence inhomogeneities. The generation stable by means Feshbach resonance techniques is also discussed.

We report a diversity of stable gap solitons in spin-orbit-coupled Bose-Einstein condensate subject to spatially periodic Zeeman field. It is shown that the can be classified by main physical symmetries they obey, i.e., with respect parity ($P$), time ($T$), and internal degree freedom, spin ($C$), inversions. The conventional gap-stripe are obtained lattices different parameters. same type but obeying exist lattice at spatial locations. $PT$ $CPT$ symmetric have antiferromagnetic structure...

Evolution of periodic matter waves in one-dimensional Bose-Einstein condensates with time-dependent scattering length is described. It shown that variation the effective nonlinearity a powerful tool for controlled generation bright and dark solitons starting waves.

We discuss localized ground states of Bose-Einstein condensates in optical lattices with attractive and repulsive three-body interactions the framework a quintic nonlinear Schr\"odinger equation which extends Gross-Pitaevskii to one dimensional case. use both variational method self-consistent approach show existence unstable excitations are similar Townes solitons cubic two dimensions. These solutions shown be located forbidden zones band structure, very close edges, separating decaying...

Exact solutions for the generalized nonlinear Schrödinger equation with inhomogeneous complex linear and potentials are found. We have found localized periodic a wide class of modulations in space nonlinearity coefficients. Examples stable unstable given. also demonstrated numerically existence dissipative breathers presence an additional parabolic trap.

We study the quantum coherent tunneling between two Bose-Einstein condensates separated through an oscillating trap potential. The cases of slow and rapid varying in time potential are considered. In case a slowly trap, we nonlinear resonances chaos oscillations relative atomic population. Using Melnikov function approach, find conditions for chaotic macroscopic quantum-tunneling phenomena to exist. Criteria onset also given. values frequency modulation amplitude which lead on population,...

We study the motion of bright matter-wave solitons in nonlinear potentials, produced by periodic or random spatial variations atomic scattering length. obtain analytical results for soliton motion, radiation matter wave, and radiative decay such configurations Bose-Einstein condensate. The stable regimes propagation are analyzed. remarkable agreement with numerical simulations Gross-Pitaevskii equation mean field interactions.

The Zeno effect is investigated for soliton type pulses in a nonlinear directional coupler with dissipation. consists increase of the transparency dissipative losses one arms. It shown that localized dissipation can lead to switching solitons between Power accompanying be fully compensated by using combination and active (in particular, parity-time-symmetric) segments.

It is shown that asymmetric waveguides with gain and loss can support a stable propagation of optical beams. This means the constants modes corresponding complex potential are real. A class such found from relation between two spectral problems. particular example an waveguide, described by hyperbolic functions, analyzed. The existence stability linear continuous families nonlinear demonstrated.

The transmissions of matter-wave solitons through linear and nonlinear inhomogeneities induced by the spatial variations trap scattering length in Bose-Einstein condensates are investigated. enhanced transmission a soliton modulation length, is exhibited. theory based on perturbed inverse transform for solitons, we show that radiation effects important. Numerical simulations Gross-Pitaevskii equation confirm theoretical predictions.

The dynamics of soliton interaction in two tunnel-coupled optical fibers as a function their phase difference Psi is analytically and numerically investigated. It shown that if = 0 or pi, no energy redistribution occurs the fibers, pulses either form coupled state (Psi pi) repulse each other separate during propagation 0). Results computer simulations under strong-coupling conditions are presented.

We study the existence and stability of solitons in quadratic nonlinear media with spatially localized ${\cal PT}$-symmetric modulation linear refractive index. Families stable one two hump are found. The properties modes bifurcating from a limit small fundamental harmonic field investigated. It is shown that branch, mode limited power. power maximum decreases strength imaginary part second can exist even above PT}$ symmetry breaking threshold. found branch undergo secondary bifurcation...

Binary mixtures of Bose-Einstein condensates (BECs) trapped in deep optical lattices and subjected to equal contributions Rashba Dresselhaus spin-orbit coupling (SOC) are investigated the presence a periodic time modulation Zeeman field. SOC tunability is explicitly demonstrated by adopting mean-field tight-binding model for BEC mixture performing an averaging approach strong limit. In this case, system can be reduced unmodulated vector discrete nonlinear Schr\"odinger equation with rescaled...

Modulational instability of a uniform two-dimensional binary Bose-Einstein condensate (BEC) in the presence quantum fluctuations is studied. The analysis based on coupled Gross-Pitaevskii equations. It shown that can induce when BEC density below threshold. dependence growth rate modulations parameters found. observed an asymmetry interaction and/or initial densities components typically decreases rate. Further development results break-up into set droplets. These droplets merge dynamically...