arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 73 records · Page 4Linked to original sources

arXiv2025

Dissipative structures in one- and two-dimensional Kerr cavities with a spatially periodic pump

The interplay of periodic driving and dissipation is a fundamental feature of nonequilibrium physics. We elaborate a scenario for the formation of dissipative multi-spot excitations (MSEs) in Kerr cavities, modeled by the one- and two-dimensional (1D and 2D) Lugiato-Lefever (LL) equations, which include a spatially periodic pump (SPP). First, we demonstrate that the SPP produces three novel exact periodic solutions of the LL equation, expressed in terms of the $\mathrm{sn}$, $\mathrm{cn}$, and $\mathrm{dn}$ elliptic functions. By means of numerical methods, we explore the modulational instability (MI) and transverse instability (TI) of the periodic states in 1D and 2D settings, respectively. In the case of the defocusing nonlinearity, the 1D MI breaks the periodic states into an array of spatiotemporal crescents. In the case of self-focusing, the 1D MI, initiated by small random perturbations, leads to establishment of a chaotic state, with the amplitude statistics featuring a long-tail probability distribution, that represents the presence of dissipative rogue waves. On the other hand, spatially periodic perturbations initiate formation of breather chains, which periodically disappear and reappear, resembling the Fermi-Pasta-Ulam-Tsingou recurrence. In the 2D regime, the TI results in the formation of an array of 2D lumps. For a given SPP strength, the exact solutions for the periodic structures are stable if the loss constant exceeds a critical value. The findings reported here provide a contribution to nonequilibrium physics in general and may find direct applications in laser physics.

physics.optics↗

arXiv2025

Vortex solitons in quasi-phase-matched photonic crystals with the third harmonic generation

We report stable composite vortex solitons in the model of a three-dimensional photonic crystal with the third-harmonic (TH) generation provided by the quasi-phase-matched quadratic nonlinearity. The photonic crystal is designed with a checkerboard structure in the $\left( x\text{,}% y\right) $ plane, while the second-order nonlinear susceptibility, $d(z)$, is modulated along the propagation direction as a chains of rectangles with two different periods. This structure can be fabricated by means of available technologies. The composite vortex solitons are built of fundamental-frequency (FF), second-harmonic (SH), and TH components, exhibiting spatial patterns which correspond to vortex with topological charges $s=1$, a quadrupole with $s=2$, and an anti-vortex structure with $s = -1$, respectively. The soliton profiles feature rhombic or square patterns, corresponding to phase-matching conditions $φ=0$ or $π$, respectively, the rhombic solitons possessing a broader stability region. From the perspective of the experimental feasibility, we show that both the rhombic and square-shaped composite vortex solitons may readily propagate in the photonic crystals over distances up to $\sim 1$ m. The TH component of the soliton with $s=\mp 1$ is produced by the cascaded nonlinear interactions, starting from the FF vortex component with $s=\pm 1$ and proceeding through the quadrupole SH one with $s=2$. These findings offer a novel approach for the creation and control of stable vortex solitons in nonlinear optics.

physics.optics↗

arXiv2025

Stable supersolids and boselets in spin-orbit-coupled Bose-Einstein condensates with three-body interactions

We explore the stability of supersolid striped waves, plane-wave boselets, and other extended states in one-dimensional spin-orbit-coupled Bose-Einstein condensates with repulsive three-body interactions (R3BIs), modeled by quintic terms in the framework of the corresponding Gross-Pitaevskii equations. In the absence of R3BIs, the extended states are susceptible to the modulational instability (MI) induced by the cubic attractive nonlinearity. Using the linearized Bogoliubov-de-Gennes equations, we identify multiple new types of MI, including baseband, passband, mixedband, and zero-wavenumber-gain ones, which give rise to deterministic rogue waves and complex nonlinear wave patterns. Our analysis reveals that R3BIs eliminate baseband and zero-wavenumber-gain MIs, forming, instead, phonon modes that enable stable boselets. Additionally, mixedband and passband MIs are suppressed, which results in a lattice-like phonon-roton mode that supports a stable supersolid phase. These stable supersolids can be realized using currently available ultracold experimental setup.

cond-mat.quant-gas↗

arXiv2025

Pure-quartic domain-wall solitons as topological bits for data transmission

Domain walls (DWs) are topological defects produced by symmetry-breaking phase transitions. Although DWs have been the subject of much work due to their fundamental physical properties, they have not been explored in optical systems with higher-order dispersion. Recent experimental and theoretical works have demonstrated that pure-quartic (PQ) solitons, with their specific energy-width scaling, arise from the interplay of the quartic group-velocity dispersion (GVD) and Kerr nonlinearity. Here, we report solutions for PQ-DW solitons for the model of optical media with the PQ GVD. The analysis demonstrates that they are stable modes. Further investigation reveals their potential as data carriers for optical telecommunications. These results broaden the variety of optical solitons maintained by diverse nonlinear media.

physics.optics↗

arXiv2025

Vortex droplets and lattice patterns in two-dimensional traps: A photonic spin-orbit-coupling perspective

In the context of the mean-field exciton-polariton (EP) theory with balanced loss and pump, we investigate the formation of lattice structures built of individual vortex-antivortex (VAV) bound states under the action of the two-dimensional harmonic-oscillator (HO) potential trap and effective spin-orbit coupling (SOC), produced by the TE-TM splitting in the polariton system. The number of VAV elements (pixels) building the structures grow with the increase of self- and cross-interaction coefficients. Depending upon their values and the trapping frequency, stable ring-shaped, circular, square-shaped, rectangular, pentagonal, hexagonal, and triangular patterns are produced, with the central site left vacant or occupied in the lattice patterns of different types. The results suggest the experimental creation of the new patterns and their possible use for the design of integrated circuits in EP setups, controlled by the strengths of the TE-TM splitting, nonlinearity, and HO trap.

physics.optics↗

arXiv2025

Solitons in Quasiperiodic Lattices with Fractional Diffraction

We study the dynamics of solitons under the action of one-dimensional quasiperiodic lattice potentials, fractional diffraction, and nonlinearity. The formation and stability of the solitons is investigated in the framework of the fractional nonlinear Schrödinger equation. By means of variational and numerical methods, we identify conditions under which stable solitons emerge, stressing the effect of the fractional diffraction on soliton properties. The reported findings contribute to the understanding of the soliton behavior in complex media, with implications for topological photonics and matter-wave dynamics in lattice potentials.

nlin.PS↗

arXiv2025

Interactions of fractional solitons with local defects: Stabilization and scattering

Stability is an essential problem in theoretical and experimental studies of solitons in nonlinear media with fractional diffraction, which is represented by the Riesz derivative with Levy index (LI) taking values LI < 2. Fractional solitons are unstable at LI smaller or equal to 1, or LI smaller or equal to 2 in uniform one-dimensional media with the cubic or quintic self-focusing, respectively. We demonstrate that, in these cases, the solitons may be effectively stabilized by pinning to a delta-functional trapping potential (attractive defect), which is a relevant setting in optical waveguides with the effective fractional diffraction. Using the respective fractional nonlinear Schroedinger equation with the delta-functional potential term, we find that, in the case of the cubic self-focusing, the fractional solitons are fully stabilized by the pinning to the defect for LI = 1, and partly stabilized for LI < 1. In the case of the quintic self-focusing, the full and partial stabilization are found for LI = 2 and LI < 2, respectively. In both cases, the instability boundary is exactly predicted by the Vakhitov-Kolokolov criterion. Unstable solitons spontaneously transform into oscillating breathers. A variational approximation (VA) is elaborated parallel to the numerical analysis, with a conclusion that the VA produces accurate results for lower LI values, i.e., stronger fractionality. In the cubic medium, collisions of traveling stable solitons with repulsive and attractive defects are addressed too, demonstrating outcomes in the form of rebound, splitting, and passage.

nlin.PS↗

arXiv2025

Solitons in Bose-Einstein Condensates with Attractive Self-Interaction on a Möbius Strip

We study the matter-wave solitons in Bose-Einstein condensate (BEC) trapped on a Möbius strip (MS), based on the respective Gross-Pitaevskii (GP) equation with the mean-field theory. In the linear regime, vortex states are characterized by quantum numbers, $n$ and $m$, corresponding to the transverse and circumferential directions, with the phase structure determined by the winding number (WN) $m$. Odd and even values of $n$ must associate, respectively, with integer and half-integer values of $m$, the latter ones requiring two cycles of motion around MS for returning to the initial phase. Using variational and numerical methods, we solve the GP equation with the attractive nonlinearity, producing a family of ground-state (GS) solitons for values of the norm below the critical one, above which the collapse sets in. Vortex solitons with $n=1,m=1$ and $% n=2,m=1/2$ are obtained in a numerical form. The vortex solitons with $% n=1,m=1$ are almost uniformly distributed in the azimuthal direction, while ones with $n=2,m=1/2$ form localized states. The Vakhitov-Kolokolov criterion and linear-stability analysis for the GS soliton solutions and vortices with $n=1,m=1$ demonstrates that they are completely stable, while the localized states with $n=2,m=1/2$ are completely unstable. Finally, the motion of solitons on the MS and the collision of two solitons are discussed.

nlin.PS↗

arXiv2025

Effects of fractional diffraction on nonlinear PT phase transitions and stability of dark solitons and vortices

The wave propagation under the action of fractional diffraction has recently drawn increasing attention in nonlinear optics. Here, we address the effect of fractional diffraction on the existence, phase transitions, and stability of dark solitons (DSs) and vortices in parity-time (PT) symmetric graded-index waveguide with self-defocusing nonlinearity. The DSs and vortices are produced by numerical solution of the corresponding one- and two-dimensional fractional nonlinear Schrödinger equations. We show that solution branches of fundamental and higher-order DSs collide pair-wise (merge) and disappear with the increase of the gain-loss strength, revealing nonlinear PT phase transitions in the waveguide. Numerically identifying the merger points, we demonstrate effects of the fractional diffraction on the phase transition.The phase transition points determine boundaries of existence regions for the DSs and vortices.The stability of the DSs and vortices is studied by means of the linearization with respect to small perturbations. Direct simulations of perturbed evolution corroborate their stability properties predicted by the analysis of small perturbations.

physics.optics↗

arXiv2025

Thermodynamics of free bosons and fermions in the hyperball

Many-particle systems pose commonly known computational challenges in quantum theory. The obstacles arise from the difficulty in finding sets of eigenvalues and eigenvectors of the underlying Hamiltonian while enforcing fermion or boson statistics, not to mention the prohibitive increase in the computational cost with the system's size. The first obvious step in this direction is to elaborate the theory for Fermi or Bose gases without inter-particle interactions. The traditional approach to the work is with the ideal gases confined in a cubic container with impenetrable walls (in arbitrary dimensions). This approach allows one to find the particle's spectra and compute all thermodynamic quantities of the confined gas. In the present work, we consider the gas confined in a spherical container (in other words, an infinitely deep spherical potential well in D dimensions), solving the corresponding Schroedinger equation using zero boundary conditions. We address the case of a finite number of particles N, either bosons or fermions, in the spherical potential box, as well as the thermodynamic limit. Owing to Weyl's relations, in the latter limit, the results do not depend on the shape of the box and thus approach the commonly known ones valid in the infinite space. Owing to the underlying SO(D) symmetry, we are dealing with particles carrying a well-defined angular momentum that, together with sorted energy eigenvalues, imparts a shell structure to the system.

quant-ph↗

arXiv2025

Multiple Temporal Compression as a method to control the generation of bright and dark solitons

Recently published works have shown that the Multiple Temporal Compression (MTC) method is a more efficient approach for generation of multiple bright solitons in stacked waveguides, in comparison to the traditional soliton-fission technique. In the present paper, we performed systematic computer simulations of the appropriate generalized nonlinear Schrödinger equation to extend the MTC method for generation of dark solitons through controlled interactions of bright solitons in waveguiding systems with the normal group-velocity dispersion. Further, the generated dark solitons are demonstrated to be useful for accurately governing the dynamics of bright solitons generation in complex systems based on stacked waveguides. Therefore, we report scenarios that provide mitigation or switching of the energy transfer during bright-soliton collisions, along with the ability of the cascaded MTC processes to increase the number of the generated solitons. These results underscore the potential of the MTC as a versatile method for managing the propagation dynamics of multiple temporal bright and dark solitons produced by a single input pulse, with possible applications for the design of optical devices.

physics.optics↗

arXiv2025

Experimental emulator of pulse dynamics in fractional nonlinear Schrödinger equation

We present a nonlinear optical platform to emulate a nonlinear \textit{Lévy waveguide} that supports the pulse propagation governed by a generalized fractional nonlinear Schrödinger equation (FNLSE). Our approach distinguishes between intra-cavity and extra-cavity regimes, exploring the interplay between the effective fractional group-velocity dispersion (FGVD) and Kerr nonlinearity. In the intra-cavity configuration, we observe stable \textit{fractional solitons} enabled by an engineered combination of the fractional and regular dispersions in the fiber cavity. The soliton pulses exhibit their specific characteristics, \textit{viz.}, "heavy tails" and a "spectral valley" in the temporal and frequency domain, respectively, highlighting the effective nonlocality introduced by FGVD. Further investigation in the extra-cavity regime reveals the generation of spectral valleys with multiple lobes, offering potential applications to the design of high-dimensional data encoding. To elucidate the spectral valleys arising from the interplay of FGVD and nonlinearity, we have developed an innovative "force" model supported by comprehensive numerical analysis. These findings open new avenues for experimental studies of spectral-temporal dynamics in fractional nonlinear systems.

physics.optics↗

arXiv2024

Tunable beam splitting via photorefractive nonlinearity and its applications in chiral waveguide induction and vortex generation

We report experimental observation and theoretical explanation of novel propagation regimes for optical beams in an artificial nonlinear material with outstanding photorefractive properties. Nondiffractive beams, which keep their shapes invariant in the free space, feature self-splitting from the middle in two separating secondary beams, due to the light-matter interaction. The splitting degree is controlled by means of a phase-pre-modulation method. We propose applications of the self-splitting to the creation of an effectively chiral waveguide and the generation of even-order vortices.

physics.optics↗

arXiv2024

Temporal localization of optical waves supported by a copropagating quasiperiodic structure

Research on time crystals concerns the spontaneous breaking of translational symmetry in time, as well as the realization of phenomena and phases known from solid-state physics in the time domain. Periodically driven systems of massive particles are widely used in these studies. In the present work, we consider a photonic system and demonstrate that stable nonlinear propagation of a strong optical wave in a fiber leads to the establishment of quasi-periodic oscillations in the electromagnetic field intensity. A second, weaker signal optical wave propagating in the fiber senses these oscillations and, as a result, undergoes exponential localization in time. This is a temporal analogue of Aubry-Andre localization. If an optical detector is placed at a certain position in the fiber, the temporal localization of the probe wave will be observed in the form of the signal which emerges and then decays as a function of time.

physics.optics↗

arXiv2024

Two-dimensional fractional discrete NLS equations: dispersion relations, rogue waves, fundamental and vortex solitons

We introduce physically relevant new models of two-dimensional (2D) fractional lattice media accounting for the interplay of fractional intersite coupling and onsite self-focusing. Our approach features novel discrete fractional operators based on an appropriately modified definition of the continuous Riesz fractional derivative. The model of the 2D isotropic lattice employs the discrete fractional Laplacian, whereas the 2D anisotropic system incorporates discrete fractional derivatives acting independently along orthogonal directions with different Lévy indices (LIs). We derive exact linear dispersion relations (DRs), and identify spectral bands that permit linear modes to exist, finding them to be similar to their continuous counterparts, apart from differences in the wavenumber range. Additionally, the modulational instability in the discrete models is studied in detail, and, akin to the linear DRs, it is found to align with the situation in continuous models. This consistency highlights the nature of our newly defined discrete fractional derivatives. Furthermore, using Gaussian inputs, we produce a variety of rogue-wave structures. By means of numerical methods, we systematically construct families of 2D fundamental and vortex solitons, and examine their stability. Fundamental solitons maintain the stability due to the discrete nature of the interactions, preventing the onset of the critical and supercritical collapse. On the other hand, vortex solitons are unstable in the isotropic lattice model. However, the anisotropic one -- in particular, its symmetric version with equal LIs acting in both directions -- maintains stable vortex solitons with winding numbers $S=1$ and $S=3$. The detailed results stress the robustness of the newly defined discrete fractional Laplacian in supporting well-defined soliton modes in the 2D lattice media.

nlin.PS↗

arXiv2024

Prediction and observation of topological modes in fractal nonlinear optics

This item from the News & Views category, to be published in Light: Science & Applications, aims to provide a summary of theoretical and experimental results recently published in Ref. [24], which demonstrate the creation of corner modes in nonlinear optical waveguides of the higher-order topological-insulator (HOTI) type. Actually, these are second-order HOTIs, in which the transverse dimension of the topologically protected edge modes is smaller than the bulk dimension (it is 2, in the case of optical waveguide) by 2, implying zero dimension of the protected modes, that are actually realized as corner or defect ones. Work [24] reports prediction and creation of various forms of the corner modes in a HOTI with a fractal transverse structure, represented by the Sierpinski gasket (SG). The self-focusing nonlinearity of the waveguide's material transforms the corner modes into corner solitons, almost all of which are stable. The solitons may be attached to external or internal corners created by the underlying SG. This N&V item offers an overview of these new findings reported in Ref. [24] and other recent works, and a brief discussion of directions for the further work on this topic.

physics.optics↗

arXiv2024

Breather bound states in a parametrically driven magnetic wire

We report the results of systematic investigation of localized dynamical states in the model of a one-dimensional magnetic wire, which is based on the Landau-Lifshitz-Gilbert (LLG) equation. The dissipative term in the LLG equation is compensated by the parametric drive imposed by the external AC magnetic field, which is uniformly applied perpendicular to the rectilinear wire. The existence and stability of the localized states is studied in the plane of the relevant control parameters, viz., the amplitude of the driving term and the detuning of its frequency from the parametric resonance. With the help of systematically performed simulations of the LLG equation, existence and stability areas are identified in the parameter plane for several species of the localized states: stationary single- and two-soliton modes, single and double breathers, drifting double breathers with spontaneously broken inner symmetry, and multi-soliton complexes. Multistability occurs in this system. The breathers emit radiation waves (which explains their drift caused by the spontaneous symmetry breaking, as it breaks the balance between the recoil from the waves emitted to left and right), while the multi-soliton complexes exhibit cycles of periodic transitions between three-, five-, and seven-soliton configurations. Dynamical characteristics of the localized states are systematically calculated too. These include, in particular, the average velocity of the asymmetric drifting modes, and the largest Lyapunov exponent, whose negative and positive values imply that the intrinsic dynamics of the respective modes is regular or chaotic, respectively.

nlin.PS↗

arXiv2024

Ground-state phase transitions in spin-1 Bose-Einstein condensates with spin-orbit coupling

We investigate phase transitions of the ground state (GS) of spin-1 Bose-Einstein condensates under the combined action of the spin-orbit coupling (SOC) and gradient magnetic field. Introducing appropariate raising and lowering operators, we exactly solve the linear system. Analyzing the obtained energy spectrum, we conclude that simultaneous variation of the magnetic-field gradient and SOC strength leads to the transition of excited states into the GS. As a result, any excited state can transition to the GS, at appropriate values of the system's parameters. The nonlinear system is solved numerically, showing that the GS phase transition, similar to the one in the linear system, still exists under the action of the repulsive nonlinearity. In the case of weak attraction, a mixed state appears near the GS transition point, while the GS transitions into an edge state under the action of strong attractive interaction.

cond-mat.quant-gas↗