arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 433 records · Page 24Linked to original sources

arXiv2012

Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices

It has been recently discovered that stabilization of two-dimensional (2D) solitons against the critical collapse in media with the cubic nonlinearity by means of nonlinear lattices (NLs) is a challenging problem. We address the 1D version of the problem, i.e., the nonlinear-Schrödinger equation (NLSE) with the quintic or cubic-quintic (CQ) terms, the coefficient in front of which is periodically modulated in space. The models may be realized in optics and Bose-Einstein condensates (BECs). Stability diagrams for the solitons are produced by means of numerical methods and analytical approximations. It is found that the sinusoidal NL stabilzes solitons supported by the quintic-only nonlinearity in a narrow stripe in the respective parameter plane, on the contrary to the case of the cubic nonlinearity in 2D, where the stabilization of solitons by smooth spatial modulations is not possible at all. The stability region is much broader in the 1D CQ model, where higher-order solitons may be stable too.

nlin.PS↗

arXiv2012

Solitons supported by spatially inhomogeneous nonlinear losses

We uncover that, in contrast to the common belief, stable dissipative solitons exist in media with uniform gain in the presence of nonuniform cubic losses, whose local strength grows with coordinate x (in one dimension) faster than |x|. The spatially-inhomogeneous absorption also supports new types of solitons, that do not exist in uniform dissipative media. In particular, single-well absorption profiles give rise to spontaneous symmetry breaking of fundamental solitons in the presence of uniform focusing nonlinearity, while stable dipoles are supported by double-well absorption landscapes. Dipole solitons also feature symmetry breaking, but under defocusing nonlinearity.

nlin.PS↗

arXiv2012

Two-dimensional solitons and vortices in media with incommensurate linear and nonlinear lattice potentials

We construct families of ordinary and gap solitons (GSs), including solitary vortices, in the two-dimensional (2D) system based on the nonlinear-SchrÄodinger/Gross-Pitaevskii equation with the 2D or quasi-1D (Q1D) periodic linear potential, combined with the periodic modulation of the cubic nonlinearity (also in the 2D or Q1D form), which is, generally, incommensurate with the linear potential, thus forming a \nonlinear quasicrystal". Stable vortices are built as complexes of four peaks with the separation between them equal to the double period of the linear potential. The system may be realized in photonic crystals or Bose-Einstein condensates (BECs). The variational approximation (VA) is applied to ordinary solitons (residing in the semi-infinite gap), and numerical methods are used to construct solitons of all the types. Stability regions are identified for soliton families in all the versions of the model.

physics.optics↗

arXiv2012

Stable nonlinear amplification of solitons without gain saturation

We demonstrate that the cubic gain applied in a localized region, which is embedded into a bulk waveguide with the cubic-quintic nonlinearity and uniform linear losses, supports stable spatial solitons in the absence of the quintic dissipation. The system, featuring the bistability between the solitons and zero state (which are separated by a family of unstable solitons), may be used as a nonlinear amplifier for optical and plasmonic solitons, which, on the contrary to previously known settings, does not require gain saturation. The results are obtained in an analytical form and corroborated by the numerical analysis.

physics.optics↗

arXiv2011

Multi-stable dissipative structures pinned to dual hot spots

We analyze the formation of one-dimensional localized patterns in a nonlinear dissipative medium including a set of two narrow "hot spots" (HSs), which carry the linear gain, local potential, cubic self-interaction, and cubic loss, while the linear loss acts in the host medium. This system can be realized, as a spatial-domain one, in optics, and also in Bose-Einstein condensates of quasi-particles in solid-state settings. Recently, exact solutions were found for localized modes pinned to the single HS represented by the delta-function. The present paper reports analytical and numerical solutions for coexisting two- and multi-peak modes, which may be symmetric or antisymmetric with respect to the underlying HS pair. Stability of the modes is explored through simulations of their perturbed evolution. The sign of the cubic nonlinearity plays a crucial role: in the case of the self-focusing, only the fundamental symmetric and antisymmetric modes, with two local peaks tacked to the HSs, and no additional peaks between them, may be stable. In this case, all the higher-order multi-peak modes, being unstable, evolve into the fundamental ones. Stability regions for the fundamental modes are reported. A more interesting situation is found in the case of the self-defocusing cubic nonlinearity, with the HS pair giving rise to a multi-stability, with up to eight coexisting stable multi-peak patterns, symmetric and antisymmetric ones. The system without the self-interaction, the nonlinearity 2 being represented only by the local cubic loss, is investigated too. This case is similar to those with the self-focusing or defocusing nonlinearity, if the linear potential of the HS is, respectively, attractive or repulsive. An additional feature of the former setting is the coexistence of the stable fundamental modes with robust breathers.

nlin.PS↗

arXiv2011

Symmetric and asymmetric solitons trapped in H-shaped potentials

We report results of numerical and analytical studies of the spontaneous symmetry breaking in solitons, both two- and one-dimensional, which are trapped in H-shaped potential profiles, built of two parallel potential troughs linked by a narrow rung in the transverse direction. This system can be implemented in self-attractive Bose-Einstein condensates (BECs), as well as in a nonlinear bulk optical waveguide.We demonstrate that the introduction of the transverse link changes the character of the symmetry-breaking bifurcation (SBB) in the system from subcritical to supercritical (in terms of the corresponding phase transition, it is a change between the first and second kinds). A noteworthy feature of the SBB in this setting is a non-monotonous dependence of the soliton's norm at the bifurcation point on the strength of the transverse link. In the full 2D system, the results are obtained in a numerical form. An exact analytical solution is found for the bifurcation in the 1D version of the model, with the transverse rung modeled by the local linear coupling between the parallel troughs with the Delta-functional longitudinal profile. Replacing the Delta-function by its finite-width Gaussian counterpart, similar results are obtained by means of the variational approximation (VA). The VA is also applied to the 1D system with a mixed linear and nonlinear transverse localized coupling. Comparison of the results produced by the different varieties of the system clearly reveals basic features of the symmetry-breaking transition in it.

cond-mat.quant-gas↗

arXiv2011

Transfer and scattering of wave packets by a nonlinear trap

In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by "nonlinear tweezers", as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of the nonlinear trap for the dragging allows one to pick up and transfer the relevant structures without grabbing surrounding "garbage". A stability border for the dragged modes is identified by means of of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy stationary modes with a divergent norm, that may be dragged by the nonlinear trap moving at a constant acceleration, are briefly considered too.

nlin.PS↗

arXiv2011

Self-trapping and splitting of bright vector solitons under inhomogeneous defocusing nonlinearities

We show that bimodal systems with a spatially nonuniform defocusing cubic nonlinearity, whose strength grows toward the periphery, can support stable two-component solitons. For a sufficiently strong XPM interaction, vector solitons with overlapping components become unstable, while stable families of solitons with spatially separated components emerge. Stable complexes with separated components may be composed not only of fundamental solitons, but of multipoles too.

physics.optics↗

arXiv2011

Dynamics of bright solitons and soliton arrays in the nonlinear Schrodinger equation with a combination of random and harmonic potentials

We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schrödinger equation (NLSE), which includes the harmonic-oscillator (HO) potential and a random potential. The equation models experimentally relevant spatially disordered settings in Bose-Einstein condensates (BECs) and nonlinear optics. First, the generation of soliton arrays from a broad initial quasi-uniform state by the modulational instability (MI) is considered, following a sudden switch of the nonlinearity from repulsive to attractive. Then, we study oscillations of a single soliton in this setting, which models a recently conducted experiment in BEC. Basic characteristics of the MI-generated array, such as the number of solitons and their mobility, are reported as functions of the strength and correlation length of the disorder, and of the total norm. For the single oscillating soliton, its survival rate is found. Main features of these dependences are explained qualitatively.

nlin.PS↗

arXiv2011

Solitons in a chain of PT-invariant dimers

Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrodinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anti-continuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear PT-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability threshold drops with the increase of the gain-loss coefficient, but it does not depend on the lattice coupling constant, nor on the soliton's velocity.

physics.optics↗

arXiv2011

Quasi-compactons in inverted nonlinear photonic crystals

We study large-amplitude one-dimensional solitary waves in photonic crystals featuring competition between linear and nonlinear lattices, with minima of the linear potential coinciding with maxima of the nonlinear pseudopotential, and vice versa (inverted nonlinear photonic crystals, INPhCs), in the case of the saturable self-focusing nonlinearity. Such crystals were recently fabricated using a mixture of SU-8 and Rhodamine-B optical materials. By means of numerical methods and analytical approximations, we find that large-amplitude solitons are broad sharply localized stable pulses (quasi-compactons, QCs). With the increase of the totalpower, P, the QC's centroid performs multiple switchings between minima and maxima of the linear potential. Unlike cubic INPhCs, the large-amplitude solitons are mobile in the medium with the saturable nonlinearity. The threshold value of the kick necessary to set the soliton in motion is found as a function of P. Collisions between moving QCs are considered too.

physics.optics↗

arXiv2011

Stability of solitons in PT-symmetric couplers

Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of the gain, loss and inter-core coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").

physics.optics↗

arXiv2011

Domain walls and vortices in linearly coupled systems

We investigate 1D and 2D radial domain-wall (DW) states in the system of two nonlinear-Schrödinger/Gross-Pitaevskii equations, which are coupled by the linear mixing and by the nonlinear XPM (cross-phase-modulation). The system has straightforward applications to two-component Bose-Einstein condensates, and to the bimodal light propagation in nonlinear optics. In the former case, the two components represent different hyperfine atomic states, while in the latter setting they correspond to orthogonal polarizations of light. Conditions guaranteeing the stability of flat continuous wave (CW) asymmetric bimodal states are established, followed by the study of families of the corresponding DW patterns. Approximate analytical solutions for the DWs are found near the point of the symmetry-breaking bifurcation of the CW states. An exact DW solution is produced for ratio 3:1 of the XPM and SPM coefficients. The DWs between flat asymmetric states, which are mirror images to each other, are completely stable, and all other species of the DWs, with zero crossings in one or two components, are fully unstable. Interactions between two DWs are considered too, and an effective potential accounting for the attraction between them is derived analytically. Direct simulations demonstrate merger and annihilation of the interacting DWs. The analysis is extended for the system including single- and double-peak external potentials. Generic solutions for trapped DWs are obtained in a numerical form, and their stability is investigated. An exact stable solution is found for the DW trapped by a single-peak potential. In the 2D geometry, stable two-component vortices are found, with topological charges s=1,2,3. Radial oscillations of annular DW-shaped pulsons, with s=0,1,2, are studied too. A linear relation between the period of the oscillations and the mean radius of the DW ring is derived analytically.

physics.optics↗

arXiv2011

Bright solitons from defocusing nonlinearities

We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of stable solitons in all three dimensions, including 1D fundamental and multihump states, 2D vortex solitons with arbitrarily high topological charges, and fundamental solitons in 3D. Solitons maintain their coherence in the state of motion, oscillating in the nonlinear potential as robust quasi-particles and colliding elastically. In addition to numerically found soliton families, particular solutions are found in an exact analytical form, and accurate approximations are developed for the entire families, including moving solitons.

physics.optics↗

arXiv2011

Algebraic bright and vortex solitons in defocusing media

We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the nonlinearity coefficient growing toward the periphery as [1+abs(r)]**a support one- and two-dimensional fundamental and higher-order bright solitons, as well as vortex solitons, with algebraically decaying tails. The energy flow of the solitons converges as long as nonlinearity growth rate exceeds the dimensionality, i.e., a>D. Fundamental solitons are always stable, while multipoles and vortices are stable if the nonlinearity growth rate is large enough.

physics.optics↗

arXiv2011

Spontaneous symmetry breaking in linearly coupled disk-shaped Bose-Einstein condensates

We study effects of tunnel coupling on a pair of parallel disk-shaped Bose-Einstein condensates with the self-attractive intrinsic nonlinearity. Each condensate is trapped in a combination of in-plane and transverse harmonic-oscillator potentials. It is shown that, depending on the self-interaction strength and tunneling coupling, the ground state of the system exhibits a phase transition which links three configurations: a symmetric one with equal numbers of atoms in the coupled condensates, an asymmetric configuration with a population imbalance (a manifestation of the macroscopic quantum self-trapping), and the collapsing state. A modification of the phase diagram of the system in the presence of vortices in the disk-shaped condensates is reported too. The study of dynamics around the stationary configurations reveals properties which strongly depend on the symmetry of the configuration.

cond-mat.quant-gas↗

arXiv2011

Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials

We introduce the two-dimensional Gross-Pitaevskii/nonlinear-Schrodinger (GP/NLS) equation with the self-focusing nonlinearity confined to two identical circles, separated or overlapped. The model can be realized in terms of Bose-Einstein condensates (BECs) and photonic-crystal fibers. Following the recent analysis of the spontaneous symmetry breaking (SSB) of localized modes trapped in 1D and 2D double-well nonlinear potentials (also known as pseudopotentials), we aim to find 2D solitons in the two-circle setting, using numerical methods and the variational approximation (VA). Well-separated circles support stable symmetric and antisymmetric solitons. The decrease of separation L between the circles leads to destabilization of the solitons. The symmetric modes undergo two SSB transitions. First, they are transformed into weakly asymmetric breathers, which is followed by a transition to single-peak modes trapped in one circle. The antisymmetric solitons perform a direct transition to the single-peak mode. The symmetric solitons are described reasonably well by the VA. For touching (L=0) and overlapping (L<0) circles, single-peak solitons are found-asymmetric ones, trapped in either circle, and symmetric solitons centered at the midpoint of the bi-circle configuration. If the overlap is weak, the symmetric soliton is unstable. It may spontaneously leap into either circle and perform shuttle motion in it. A region of stability of the symmetric solitons appears with the increase of the overlap degree. In the case of a moderately strong overlap, another SSB effect is found, in the form of a pair of symmetry-breaking and restoring bifurcations which link families of the symmetric and asymmetric solitons.

nlin.PS↗

arXiv2011

Gap solitons in elongated geometries: the one-dimensional Gross-Pitaevskii equation and beyond

We report results of a systematic analysis of matter-wave gap solitons (GSs) in three-dimensional self-repulsive Bose-Einstein condensates (BECs) loaded into a combination of a cigar-shaped trap and axial optical-lattice (OL) potential. Basic cases of the strong, intermediate, and weak radial (transverse) confinement are considered, as well as settings with shallow and deep OL potentials. Only in the case of the shallow lattice combined with tight radial confinement, which actually has little relevance to realistic experimental conditions, does the usual one-dimensional (1D) cubic Gross-Pitaevskii equation (GPE) furnish a sufficiently accurate description of GSs. However, the effective 1D equation with the nonpolynomial nonlinearity, derived in Ref. [Phys. Rev. A \textbf{77}, 013617 (2008)], provides for quite an accurate approximation for the GSs in all cases, including the situation with weak transverse confinement, when the soliton's shape includes a considerable contribution from higher-order transverse modes, in addition to the usual ground-state wave function of the respective harmonic oscillator. Both fundamental GSs and their multipeak bound states are considered. The stability is analyzed by means of systematic simulations. It is concluded that almost all the fundamental GSs are stable, while their bound states may be stable if the underlying OL potential is deep enough.

cond-mat.quant-gas↗