arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 469 records · Page 26Linked to original sources

arXiv2010

Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with a spatially modulated nonlinearity

We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite number of exact soliton solutions in terms of the Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite bandgap of the optical-lattice-induced spectrum. Starting from the exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.

cond-mat.quant-gas↗

arXiv2010

Two - dimensional solitons in media with the stripe - shaped nonlinearity modulation

We introduce a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane. The model can be realized in terms of nonlinear optics (in the spatial and temporal domains alike) and BEC. In recent works, it was concluded that search for stable 2D solitons in models with a spatially localized self-attractive nonlinearity is a challenging problem. We make use of the variational approximation (VA) and numerical methods to investigate conditions for the existence and stability of solitons in the present setting. The result crucially depends on the transverse shape of the stripe: while the rectangular profile supports stable 2D solitons, its smooth Gaussian-shaped counterpart makes all the solitons unstable. The double stripe with the rectangular profile admit stable solitons of three distinct types: symmetric and asymmetric ones with a single peak, and double-peak symmetric solitons. The shape and stability of single-peak solitons of either type are accurately predicted by the VA. Collisions between stable solitons are briefly considered too, by means of direct simulations. Depending on the relative velocity we observe excitation, decay or catastrophic self focusing.

nlin.PS↗

arXiv2010

Exact exact solutions of the Gross-Pitaevskii equation for stable vortex modes

We construct exact solutions of the Gross-Pitaevskii equation for solitary vortices, and approximate ones for fundamental solitons, in 2D models of Bose-Einstein condensates with a spatially modulated nonlinearity of either sign and a harmonic trapping potential. The number of vortex-soliton (VS) modes is determined by the discrete energy spectrum of a related linear Schrödinger equation. The VS families in the system with the attractive and repulsive nonlinearity are mutually complementary. \emph{% Stable} VSs with vorticity $S\geq 2$ and those corresponding to higher-order radial states are reported for the first time, in the case of the attraction and repulsion, respectively.

cond-mat.quant-gas↗

arXiv2010

Gap solitons in optical lattices embedded into nonlocal media

We analyze the existence, stability, and mobility of gap solitons (GSs) in a periodic photonic structure built into a nonlocal self-defocusing medium. Counter-intuitively, the GSs are supported even by a highly nonlocal nonlinearity, which makes the system quasi-linear. Unlike local models, the variational approximation (VA) predicts the GSs in a good agreement with numerical findings, due to the suppression of undulating tails of the solitons.

physics.optics↗

arXiv2010

Collapse suppression and stabilization of dipole solitons in two-dimensional media with anisotropic semi-local nonlinearity

We consider the impact of anisotropic nonlocality on the arrest of the collapse and stabilization of dipole-mode (DM) solitons in two-dimensional (2D) models of optical media with the diffusive nonlinearity. The nonlocal nonlinearity is made anisotropic through elliptic diffusivity. The medium becomes semi-local in the limit case of 1D diffusivity. Families of fundamental and DM solitons are found by means of the variational approximation (VA) and in a numerical form. We demonstrate that the collapse of 2D beams is arrested even in the semi-local system. The anisotropic nonlocality readily stabilizes the DM solitons, which are completely unstable in the isotropic medium.

physics.optics↗

arXiv2010

The inverse problem for the Gross - Pitaevskii equation

Two different methods are proposed for the generation of wide classes of exact solutions to the stationary Gross - Pitaevskii equation (GPE). The first method, suggested by the work by Kondrat'ev and Miller (1966), applies to one-dimensional (1D) GPE. It is based on the similarity between the GPE and the integrable Gardner equation, all solutions of the latter equation (both stationary and nonstationary ones) generating exact solutions to the GPE, with the potential function proportional to the corresponding solutions. The second method is based on the "inverse problem" for the GPE, i.e. construction of a potential function which provides a desirable solution to the equation. Systematic results are presented for 1D and 2D cases. Both methods are illustrated by a variety of localized solutions, including solitary vortices, for both attractive and repulsive nonlinearity in the GPE. The stability of the 1D solutions is tested by direct simulations of the time-dependent GPE.

cond-mat.quant-gas↗

arXiv2010

Two-dimensional gap solitons in elliptic-lattice potentials

We study two-dimensional (2D) matter-wave gap solitons trapped in an elliptically deformed concentric lattice potential, within the framework of the Gross-Pitaevskii equation (GPE) with self-attraction or self-repulsion. For a fixed eccentricity of the lattice, soliton families are found in both the repulsive and attractive models. In the former case, the analysis reveals two kinds of gap solitons trapped in the first oval trough (the ring-shaped potential minimum closest to the center): elliptic annular solitons (EASs), and double solitons (DSs), which are formed by two tightly localized density peaks located at diametrically opposite points of the trough, with zero phase difference between them. With the decrease of the norm, the density distribution in the EAS along the azimuthal direction changes from nearly-uniform to double-peaked and, eventually, to the DS. In the attractive model, there exist only DSs in the oval trough, while EASs are not found. All such solitons without the angular momentum (l = 0) are fully stable. For l is not equal to 0, vortical solitons - both EASs with a sufficiently large norm (in the repulsive model) and DSs (in models with both signs of the nonlinearity) - are quasi-stable, exhibiting rocking motion in the elliptic trough (we consider the cases of l=1 and l=2). At smaller values of the norm, the vortical annular solitons (in the repulsive model) are unstable. Stable fundamental solitons trapped in the central potential well are investigated too, in both the attractive and repulsive models, by means of the variational approximation and numerical methods.

nlin.PS↗

arXiv2010

Vortices and ring dark solitons in nonlinear amplifying waveguides

We consider the generation and propagation of (2+1)-dimensional beams in a nonlinear waveguide with the linear gain. Simple self-similar evolution of the beams is achieved at the asymptotic stage, if the input beams represent the fundamental mode. On the contrary, if they carry vorticity or amplitude nodes (or phase slips), vortex tori and ring dark solitons (RDSs) are generated, featuring another type of the self-similar evolution, with an exponentially shrinking vortex core or notch of the RDS. Numerical and analytical considerations reveal that these self-similar structures are robust entities in amplifying waveguides, being \emph{stable} against azimuthal perturbations.

physics.optics↗

arXiv2010

Solitons in combined linear and nonlinear lattice potentials

We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons. Under the direct commensurability (equal periods of the lattices, the family of ordinary solitons is similar to its counterpart in the free space. The situation is different in the case of the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or incommensurability. In those cases, there is an existence threshold for the solitons, and the scaling relation between their amplitude and width is different from that in the free space. GS families demonstrate a bistability, unless the direct commensurability takes place. Specific scaling relations are found for them too. Ordinary solitons can be readily set in motion by kicking. GSs are mobile too, featuring inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion, while the stability of GS families follows an inverted ("anti-VK") criterion, which is explained by means of the averaging approximation.

nlin.PS↗

arXiv2009

Two-dimensional discrete solitons in dipolar Bose-Einstein condensates

We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disk's plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, that differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying 3D Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial.

nlin.PS↗

arXiv2009

Vector solitons in nonlinear lattices

We consider two-component solitons in a medium with a periodic modulation of the nonlinear coefficient. The modulation enables the existence of complex multihump vector states. In particular, vector solitons composed of dipole and fundamental, or dipole and even double-hump components exist and may be stable. Families of unstable scalar solitons can be stabilized in the vectorial form, due to the coupling to a stable second component.

physics.optics↗

arXiv2009

Entanglement generation by collisions of quantum solitons

We present analytic expressions describing generation of the entanglement in collisions of initially uncorrelated quantum solitons. The results, obtained by means of the Born's approximation (for fast solitons), are valid for both integrable and non-integrable quasi-one-dimensional systems supporting soliton states.

cond-mat.other↗

arXiv2009

Stabilization of multi-beam necklace solitons in circular arrays with spatially modulated nonlinearity

We address necklace solitons supported by circular waveguide arrays with out-of-phase modulation of nonlinearity and linear refractive index. Such two-dimensional necklace solitons appear as rings of multiple out-of-phase bright spots. We show that necklace solitons are stable if their peak intensity is low or moderate and that the domain of stability shrinks with increasing nonlinearity modulation depth. However, we find that the stability domains expand with increasing number of necklace spots.

physics.optics↗

arXiv2009

Single- and multi-peak solitons in two-component models of metamaterials and photonic crystals

We report results of the study of solitons in a system of two nonlinear-Schrodinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials(MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations with equal GVD coefficients, which generate only simple single-peak solitons, the present model gives rise to families of solitons with complex shapes, which feature extended oscillatory tails and/or a double-peak structure at the center. Regions of existence are identified for single- and double-peak bimodal solitons, demonstrating a broad bistability in the system. Behind the existence border, they degenerate into single-component solutions. Direct simulations demonstrate stability of the solitons in the entire existence regions. Effects of the group-velocity mismatch (GVM) and optical loss are considered too. It is demonstrated that the solitons can be stabilized against the GVM by means of the respective "management" scheme. Under the action of the loss, complex shapes of the solitons degenerate into simple ones, but periodic compensation of the loss supports the complexity.

nlin.PS↗

arXiv2009

Intrinsic localized modes in parametrically-driven arrays of nonlinear resonators

We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically-driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schroedinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-Landau equation), which is derived directly from the underlying equations of motion of the coupled resonators, using the method of multiple scales. We investigate the creation, stability, and interaction of ILMs, show that they can form bound states, and that under certain conditions one ILM can split into two. Our findings are confirmed by simulations of the underlying equations of motion of the resonators, suggesting possible experimental tests of the theory.

cond-mat.mes-hall↗

arXiv2009

Solitons and solitary vortices in "pancake"-shaped Bose-Einstein condensates

We study fundamental and vortical solitons in disk-morphed Bose-Einstein condensates (BECs) subject to strong confinement along the axial direction. Starting from the three-dimensional (3D) Gross-Pitaevskii equation (GPE), we proceed to an effective 2D nonpolynomial Schroeodinger equation (NPSE) derived by means of the integration over the axial coordinate. Results produced by the latter equation are in very good agreement with those obtained from the full 3D GPE, including cases when the formal 2D equation with the cubic nonlinearity is unreliable. The 2D NPSE is used to predict density profiles and dynamical stability of repulsive and attractive BECs with zero and finite topological charge in various planar trapping configurations, including the axisymmetric harmonic confinement and 1D periodic potential. In particular, we find a stable dynamical regime that was not reported before, viz., periodic splitting and recombination of trapped vortices with topological charge 2 or 3 in the self-attractive BEC.

cond-mat.quant-gas↗

arXiv2009

Solitons in quasi one-dimensional Bose-Einstein condensates with competing dipolar and local interactions

We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free space, and in the presence of an optical lattice (OL). Free-space solitons may exist with an arbitrarily weak local attraction if the strength of the DD repulsion is fixed. In the case of the DD attraction, solitons do not exist beyond a maximum value of the local-repulsion strength. In the system which includes the OL, a stability region for \textit{subfundamental solitons} (SFSs) is found in the second finite bandgap. For the existence of gap solitons (GSs) under the attractive DD interaction, the contact repulsion must be strong enough. In the opposite case of the DD repulsion, GSs exist if the contact attraction is not too strong. Collisions between solitons in the free space are studied too. In the case of the local attraction, they merge or pass through each other at small and large velocities, respectively. In the presence of the local repulsion, slowly moving solitons bounce from each other.

nlin.PS↗

arXiv2009

Interactions between two-dimensional solitons in the diffractive-diffusive Ginzburg-Landau equation with the cubic-quintic nonlinearity

We report results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg- Landau equation (CGLE) with the cubic-quintic (CQ) combination of gain and loss terms. The equation may be realized as a model of a laser cavity which includes the spatial diffraction, together with the anomalous group-velocity dispersion (GVD) and spectral filtering acting in the temporal direction. Collisions between solitons are possible due to the Galilean invariance along the spatial axis. Outcomes of the collisions are identified by varying the GVD coefficient, D, and the collision "velocity" (actually, it is the spatial slope of the soliton's trajectory). At small velocities, two or three in-phase solitons merge into a single standing one. At larger velocities, both in-phase soliton pairs and pairs of solitons with opposite signs suffer a transition into a delocalized chaotic state. At still larger velocities, all collisions become quasi-elastic. A new outcome is revealed by collisions between slow solitons with opposite signs: they self-trap into persistent wobbling dipoles, which are found in two modifications (horizontal at smaller D, and vertical if D is larger (the horizontal ones resemble "zigzag" bound states of two solitons known in the 1D CGL equation of the CQ type). Collisions between solitons with a finite mismatch between their trajectories are studied too.

nlin.PS↗