arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 181 records · Page 10Linked to original sources

arXiv2021

Symmetry-breaking bifurcations and ghost states in the fractional nonlinear Schrödinger equation with a PT-symmetric potential

We report symmetry-breaking and restoring bifurcations of solitons in a fractional Schrödinger equation with the cubic or cubic-quintic (CQ) nonlinearity and a parity-time (PT)-symmetric potential, which may be realized in optical cavities. Solitons are destabilized at the bifurcation point, and, in the case of the CQ nonlinearity, the stability is restored by an inverse bifurcation. Two mutually-conjugate branches of ghost states (GSs), with complex propagation constants, are created by the bifurcation, solely in the case of the fractional diffraction. While GSs are not true solutions, direct simulations confirm that their shapes and results of their stability analysis provide a blueprint for the evolution of genuine localized modes in the system.

nlin.PS↗

arXiv2021

A quasi-periodic route to chaos in a parametrically driven nonlinear medium

Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of damped nonlinear oscillators, we investigate a route to spatiotemporal chaos emerging from standing waves. The route from the stationary to the chaotic state proceeds through quasiperiodic dynamics. The standing wave undergoes the onset of oscillatory instability, which subsequently exhibits a different critical frequency, from which the complexity originates. A suitable amplitude equation, valid close to the parametric resonance, makes it possible to produce universe results. The respective phase-space structure and bifurcation diagrams are produced in a numerical form. We characterize the relevant dynamical regimes by means of the largest Lyapunov exponent, the power spectrum, and the evolution of the total intensity of the wave field.

nlin.CD↗

arXiv2021

Singular and regular vortices on top of a background pulled to the center

A recent analysis has revealed singular but physically relevant 2D localized vortex states with density ~ 1/r^{4/3} at r --> 0 and a convergent total norm, which are maintained by the interplay of the potential of the attraction to the center, ~ -1/r^2, and a self-repulsive quartic nonlinearity, produced by the Lee-Huang-Yang correction to the mean-field dynamics of Bose-Einstein condensates. In optics, a similar setting, with the density singularity ~ 1/r, is realized with the help of quintic self-defocusing. Here we present physically relevant antidark singular-vortex states in these systems, existing on top of a flat background. Numerical solutions for them are very accurately approximated by the Thomas-Fermi wave function. Their stability exactly obeys an analytical criterion derived for small perturbations. It is demonstrated that the singular vortices can be excited by the input in the form of ordinary nonsingular vortices, hence the singular modes can be created in the experiment. We also consider regular (dark) vortices maintained by the flat background, under the action of the repulsive central potential ~ +1/r^2. The dark modes with vorticities l = 0 and l = 1 are completely stable. In the case when the central potential is attractive, but the effective one, which includes the centrifugal term, is repulsive, and a weak trapping potential ~ r^2 is added, dark vortices with l = 1 feature an intricate pattern of alternating stability and instability regions. Under the action of the instability, states with l = 1 travel along tangled trajectories, which stay in a finite area defined by the trap. The analysis is also reported for dark vortices with l = 2, which feature a complex structure of alternating intervals of stability and instability against splitting. Lastly, simple but novel flat vortices are found at the border between the anidark and dark ones.

cond-mat.quant-gas↗

arXiv2021

Propagation dynamics of radially polarized symmetric Airy beams in the fractional Schrödinger equation

We analyze the propagation dynamics of radially polarized symmetric Airy beams (R-SABs) in a (2+1)-dimensional optical system with fractional diffraction, modeled by the fractional Schrödinger equation (FSE) characterized by the Lévy index. The autofocusing effect featured by such beams becomes stronger, while the focal length becomes shorter, with the increase of . The effect of the intrinsic vorticity on the autofocusing dynamics of the beams is considered too. Then, the ability of R-SABs to capture nano-particles by means of radiation forces is explored, and multiple capture positions emerging in the course of the propagation are identified. Finally, we find that the propagation of the vortical R-SABs with an off-axis shift leads to rupture of the ring-shaped pattern of the power-density distribution.

physics.optics↗

arXiv2021

Bubbles and W-shaped solitons in Kerr media with fractional diffraction

We demonstrate that, with the help of a Gaussian potential barrier, dark modes in the form of a local depression ("bubbles") can be supported by the repulsive Kerr nonlinearity in combination with fractional dimension. Similarly, W-shaped modes are supported by a double potential barrier. Families of the modes are constructed in a numerical form, and also by means of the Thomas-Fermi and variational approximations. All these modes are stable, which is predicted by computation of eigenvalues for small perturbations and confirmed by direct numerical simulations.

nlin.PS↗

arXiv2021

Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension

We construct families of fundamental, dipole, and tripole solitons in the fractional Schrödinger equation (FSE)\ incorporating self-focusing cubic and defocusing quintic terms modulated by factors $\cos ^{2}x$ and $\sin^{2}x$, respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The shapes and stability of all the solitons strongly depend on the Lévy index (LI)\ that determines the FSE fractionality. Stability areas are identified in the plane of LI and propagation constant by means of numerical methods, and some results are explained with the help of an analytical approximation. The stability areas are broadest for the fundamental solitons and narrowest for the tripoles.

nlin.PS↗

arXiv2021

Nonlinear dynamics of wave packets in tunnel-coupled harmonic-oscillator traps

We consider a two-component linearly-coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap acting in both components, we consider Josephson oscillations (JO) initiated by an input in the form of the HO's ground state (GS) or dipole mode (DM), placed in one component. With the increase of the strength of the self-focusing nonlinearity, spontaneous symmetry breaking (SSB) between the components takes place in the dynamical JO state. Under still stronger nonlinearity, the regular JO initiated by the GS input carry over into a chaotic dynamical state. For the DM input, the chaotization happens at smaller powers than for the GS, which is followed by SSB at a slightly stronger nonlinearity. In the system with the defocusing nonlinearity, SSB does not take place, and dynamical chaos occurs in a small area of the parameter space. In the asymmetric half-trapped system, with the HO potential applied to a single component, we first focus on the spectrum of confined binary modes in the linearized system. The spectrum is found analytically in the limits of weak and strong inter-component coupling, and numerically in the general case. Under the action of the coupling, the existence region of the confined modes shrinks for GSs and expands for DMs. In the full nonlinear system, the existence region for confined modes is identified in the numerical form. They are constructed too by means of the Thomas-Fermi approximation, in the case of the defocusing nonlinearity. Lastly, particular (non-generic) exact analytical solutions for confined modes, including vortices, in one- and two-dimensional asymmetric linearized systems are found. They represent bound states in the continuum.

nlin.PS↗

arXiv2021

Modulational instability and soliton generation in chiral Bose-Einstein condensates with zero-energy nonlinearity

By means of analytical and numerical methods, we address the modulational instability (MI) in chiral condensates governed by the Gross-Pitaevskiiequation including the current nonlinearity. The analysis shows that this nonlinearity partly suppresses off the MI driven by the cubic self-focusing, although the current nonlinearity is not represented in the system's energy (although it modifies the momentum), hence it may be considered as zero-energy nonlinearity. Direct simulations demonstrate generation of trains of stochastically interacting chiral solitons by MI. In the ring-shaped setup, the MI creates a single traveling solitary wave. The sign of the current nonlinearity determines the direction of propagation of the emerging solitons.

cond-mat.quant-gas↗

arXiv2021

Embedded solitons in second-harmonic-generating lattices

Embedded solitons are exceptional modes in nonlinear-wave systems with the propagation constant falling in the system's propagation band. An especially challenging topic is seeking for such modes in nonlinear dynamical lattices (discrete systems). We address this problem for a system of coupled discrete equations modeling the light propagation in an array of tunnel-coupled waveguides with a combination of intrinsic quadratic (second-harmonic-generating) and cubic nonlinearities. Solutions for discrete embedded solitons (DESs) are constructed by means of two analytical approximations, adjusted, severally, for broad and narrow DESs, and in a systematic form with the help of numerical calculations. DESs of several types, including ones with identical and opposite signs of their fundamental-frequency and second-harmonic components, are produced. In the most relevant case of narrow DESs, the analytical approximation produces very accurate results, in comparison with the numerical findings. In this case, the DES branch extends from the propagation band into a semi-infinite gap as a family of regular discrete solitons. The study of stability of DESs demonstrates that, in addition to ones featuring the well-known property of semi-stability, there are linearly stable DESs which are genuinely robust modes.

nlin.PS↗

arXiv2021

Semidiscrete vortex solitons

We demonstrate a possibility of the creation of stable optical solitons combining one continuous and one discrete coordinate, with embedded vorticity, in an array of planar waveguides with intrinsic cubic-quintic nonlinearity. The same system may be realized in terms of the spatiotemporal light propagation in an array of tunnel-coupled optical fibers with the cubic-quintic nonlinearity. In contrast with zero-vorticity states, semidiscrete vortex solitons do not exist without the quintic term in the nonlinearity. Two types of the solitons, \emph{viz.}, intersite- and onsite-centered ones (IC and OC, respectively), with even and odd numbers $N$ of actually excited sites in the discrete direction, are identified. We consider the modes carrying the embedded vorticity $S=1$ and $2$. In accordance with their symmetry, the vortex solitons of the OC type exhibit an intrinsic core, while the IC solitons with a small $N$ may have a coreless structure. Facilitating their creation in the experiment, the modes reported in the present work may be much more compact states than their counterparts considered in other systems, and they feature strong anisotropy. They can be set in motion in the discrete direction, provided that the coupling constant exceeds a certain minimum value. Collisions between moving vortex solitons are considered too.

nlin.PS↗

arXiv2021

External light control of three-dimensional ultrashort far-infrared pulses in an inhomogeneous array of carbon nanotubes

We present a study of the propagation of three-dimensional (3D) bipolar electromagnetic ultrashort pulses in an inhomogeneous array of semiconductor carbon nanotubes (CNTs) in the presence of a control high-frequency (HF) electric field. The inhomogeneity is present in the form of a layer with an increased concentration of conduction electrons, which acts as a barrier for the propagation of ultrashort electromagnetic pulses through the CNT array. The dynamics of the pulse is described by a nonlinear equation for the vector potential of the electromagnetic field (it takes the form of a 3D generalization of the sine-Gordon equation), derived from the Maxwell's equations and averaged over the period of the HF control field. By means of systematic simulations, we demonstrate that, depending on the amplitude and frequency of the HF control, the ultrashort pulse approaching the barrier layer either passes it or bounces back. The layer's transmissivity for the incident pulse is significantly affected by the amplitude and frequency of the HF control field, with the reflection coefficient nearly vanishing in intervals that make up a discrete set of transparency windows, which resembles the effect of the electromagnetically-induced transparency. Having passed the barrier, the ultrashort pulse continues to propagate, keeping its spatiotemporal integrity. The results may be used for the design of soliton valves, with the transmissivity of the soliton stream accurately controlled by the HF field.

physics.optics↗

arXiv2020

Rogue waves and lumps on the non-zero background in the PT -symmetric nonlocal Maccari system

In this paper, the PT -symmetric version of the Maccari system is introduced, which can be regarded as a two-dimensional generalization of the defocusing nonlocal nonlinear Schrodinger equation. Various exact solutions of the nonlocal Maccari system are obtained by means of the Hirota bilinear method, long-wave limit, and Kadomtsev-Petviashvili (KP) hierarchy method. Bilinear forms of the nonlocal Maccari system are derived for the first time. Simultaneously, a new nonlocal Davey-Stewartson-type equation is derived. Solutions for breathers and breathers on top of periodic line waves are obtained through the bilinear form of the nonlocal Maccari system. Hyperbolic line rogue-wave solutions and semi-rational ones, composed of hyperbolic line rogue wave and periodic line waves are also derived in the long-wave limit. The semi-rational solutions exhibit a unique dynamical behavior. Additionally, general line soliton solutions on constant background are generated by restricting different tau-functions of the KP hierarchy, combined with the Hirota bilinear method. These solutions exhibit elastic collisions, some of which have never been reported before in nonlocal systems. Additionally, the semi-rational solutions, namely (i) fusion of line solitons and lumps into line solitons, and (ii) fission of line solitons into lumps and line solitons, are put forward in terms of the KP hierarchy. These novel semi-rational solutions reduce to 2N-lump solutions of the nonlocal Maccari system with appropriate parameters. Finally, different characteristics of exact solutions for the nonlocal Maccari system are summarized. These new results enrich the structure of waves in nonlocal nonlinear systems, and help to understand new physical phenomena.

nlin.SI↗

arXiv2020

Quantum fluctuations of the center-of-mass and relative parameters of NLS breathers

We study quantum fluctuations of macroscopic parameters of an NLS breathers, i.e., the second-order soliton solution of the nonlinear Schrödinger equation. Uncertainty relations for the parameters are derived and compared to similar relations for fundamental solitons. We compare two models for the state of the quantum field of fluctuations surrounding the classical field of the Bose-Einstein condensate: a conventionally used, computationally convenient "white noise", and a correlated noise which assumes that the breather has been created from a fundamental soliton, by means of the application of the factor-of-four quench of the nonlinearity strength. Theoretical methods used in the work are well suited for a large number of particles, $N$. We thus confirm the possibility of experimental observation of macroscopic quantum fluctuations, which is suggested by an extrapolation to large $N$ of recently reported low-$N$ Bethe-ansatz results [Phys. Rev. Lett. 119 220401 (2017)].

cond-mat.quant-gas↗

arXiv2020

Rotating azimuthons in dissipative Kerr media excited by superpositions of Bessel beams

We report the existence of persistently rotating azimuthons in media with self-focusing Kerr and absorption nonlinearities. The nonlinear loss is balanced by power influx from the peripheral reservoir stored in slowly decaying tails of the azimuthons. These modes are excited by a superposition of two Bessel beams with opposite vorticities, $\pm s$, and slightly different conicities. The excited azimuthon exhibits opposite vorticity in its center to that of the input Bessel-beam superposition due to spontaneous inversion of the topological charge in the course of the azimuthon formation. Unlike azimuthons in loss-free media, number $N$ of rotating intensity maxima and $s$ are not mutually independent, being related by $N=2s$. The robustness of the rotating azimuthons is enhanced in comparison to similar static dissipative patterns. They can be excited in almost any transparent material, in the range of intensities for which the nonlinear absorption, induced by multiphoton absorption, is relevant. Close to the ionization threshold, the rotating azimuthons reproduce recently observed helical filaments of light in air and CS$_{2}$.

physics.optics↗

arXiv2020

Propagation dynamics of abruptly autofocusing circular Airy-Gaussian vortex beams in the fractional Schrödinger equation

We introduce axisymmetric Airy-Gaussian vortex beams in a model of an optical system based on the (2+1)-dimensional fractional Schrödinger equation, characterized by its Lévy index (LI). By means of numerical methods, we explore propagation dynamics of the beams with vorticities from 0 to 4. The propagation leads to abrupt autofocusing, followed by its reversal (rebound from the center). It is shown that LI, the relative width of the Airy and Gaussian factors, and the vorticity determine properties of the autofocusing dynamics, including the focusing distance, radius of the focal light spot, and peak intensity at the focus. A maximum of the peak intensity is attained at intermediate values of LI, close to LI=1.4 . Dynamics of the abrupt autofocusing of Airy-Gaussian beams carrying vortex pairs (split double vortices) is considered too.

nlin.PS↗

arXiv2020

Spatiotemporal solitons in dispersion-managed multimode fibers

We develop the scheme of dispersion management (DM) for three-dimensional (3D) solitons in a multimode optical fiber. It is modeled by the parabolic confining potential acting in the transverse plane in combination with the cubic self-focusing. The DM map is adopted in the form of alternating segments with anomalous and normal group-velocity dispersion. Previously, temporal DM solitons were studied in detail in single-mode fibers, and some solutions for 2D spatiotemporal "light bullets", stabilized by DM, were found in the model of a planar waveguide. By means of numerical methods, we demonstrate that stability of the 3D spatiotemporal solitons is determined by the usual DM-strength parameter, $S$: they are quasi-stable at $ S S_{0}$. Stable vortex solitons are constructed too. We also consider collisions between the 3D solitons, in both axial and transverse directions. The interactions are quasi-elastic, including periodic collisions between solitons which perform shuttle motion in the transverse plane.

physics.optics↗

arXiv2020

Spatiotemporal engineering of matter-wave solitons in Bose-Einstein condensates

Since the realization of Bose-Einstein condensates (BECs) in optical potentials, intensive experimental and theoretical investigations have been carried out for matter-wave solitons, coherent structures, modulational instability (MI), and nonlinear excitation of BEC matter waves, making them objects of fundamental interest in the vast realm of nonlinear physics and soft condensed-matter physics. Ubiquitous models, which are relevant to the description of diverse nonlinear media are provided by the nonlinear Schrodinger (NLS), alias Gross-Pitaevskii (GP) equations. In many settings, nontrivial solitons and coherent structures, which do not exist or are unstable in free space, can be created or stabilized by means of various management techniques, which are represented by NLS and GP equations with spatiotemporal coefficients in front of linear or nonlinear terms. Developing this direction of research in various settings, efficient schemes of the spatiotemporal modulation of coefficients in the NLS/GP equations have been designed to engineer desirable robust nonlinear modes. This direction and related ones are the main topic of the present review. A broad and important theme is the creation and control of 1D solitons in BEC by means of combination of the temporal or spatial modulation of the nonlinearity strength and a time-varying trapping potential. An essential ramification of this topic is analytical and numerical analysis of MI of continuous-wave states, and control of the nonlinear development of MI. In addition to that, the review also includes some topics that do not directly include spatiotemporal modulation but address physically important phenomena which demonstrate similar soliton dynamics. These are soliton motion in binary BEC, three-component solitons in spinor BEC, and dynamics of two-component solitons under the action of spin-orbit coupling.

nlin.PS↗

arXiv2020

The family of quantum droplets keeps expanding

This is an item in the "View and Perspective" category, which presents a brief overview of particular aspects of the topic of "quantum droplets". It is linked to a new theoretical paper, "Quantum droplets in two-dimensional optical lattices", which will be published in Frontiers of Physics (Ref. [21] in the current preprint).

cond-mat.quant-gas↗