arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 37 records · Page 2Linked to original sources

arXiv2026

Toroidal helical pulses

Toroidal topologies and helicity are pervasive in nature and hold basic importance in scientific research. In particular, the interplay between these features gives rise to fascinating toroidal helical electromagnetic excitations. Here, we present a theoretical framework and experimental realization to introduce a family of toroidal helical pulses, exploring the intersection of the helicity and propagating toroidal modes. For this purpose, we propose a configuration combining a coaxial horn emitter and an equiangular spiral grating to directly generate such single-cycle pulses. In addition to their inherent non-transverse toroidal topology and space-time nonseparability, such pulses also possess controllable helicity. This work gives rise to a helical version of propagating toroidal electrodynamics, thereby paving the way for advanced applications, such as nontrivial light-matter interactions and data transfer.

physics.optics↗

arXiv2026

Parametrically driven pure-quartic solitons

Parametrically driven solitons are self-trapped modes in various physical settings, including optics, magnetics, etc. So far, the analysis was focused on the existence, stability, and dynamics of such solitons in systems including the second-order group-velocity dispersion (GVD), linear loss, parametric gain, and cubic nonlinearity. Here, we report the existence of quiescent parametrically driven pure-quartic solitons (PDPQSs) in the full system, and moving PDPQSs in the absence of losses. A systematic analysis reveals stability domains for the solitons in the system's parameter space. Evolution of unstable states is explored too, and it is demonstrated that collisions between traveling stable PDPQSs are elastic.

physics.optics↗

arXiv2026

Bound states of solitons in fiber lasers

This article presents a systematic review of theoretical and experimental findings for bound states of two and several dissipative solitons in fiber lasers. The theoretical basis underlying the formation and stabilization of soliton molecules in the fibers, which is provided by the complex Ginzburg-Landau equations and bound states of such equations, is presented in necessary detail, which is followed by a detailed presentation of experimental findings, including very recent ones. In particular, included are the results for the multi-soliton bound states in the fibers, as well as for the bound states in the temporal and frequency domains, single-component (scalar) and two-component (vector), two- and multi-soliton modes, as well as for bound states of spatiotemporal dissipative solitons in the lasers based on multimode fibers.

physics.optics↗

arXiv2026

The bulk modulus of three-dimensional quantum droplets

Quantum droplets (QDs), formed by ultradilute quantum fluids under the action of the Lee-Huang-Yang (LHY) effect, provide a unique platform for investigating a wide range of macroscopic quantum effects. Recent studies of QDs' breathing modes and collisional dynamics have revealed their compressibility and extensibility, which suggests that their elasticity parameters can be identified. In this work we derive the elastic bulk modulus (BM) of QDs by means of theoretical analysis and numerical simulations and establish a relation between the BM and the eigenfrequency of the QD's intrinsic vibrations. The analysis reveals the dependence of the QD's elasticity on the particle number and the strength of interparticle interactions. We additionally provide a realistic estimate of the bulk modulus for the system, yielding a concrete physical value that may serve as a reference for future experimental measurements. Taken together, these results also point to possibilities for realizing elastic media governed by the LHY effect.

cond-mat.quant-gas↗

arXiv2026

Stable high-order solitons in spiral potentials

We present a comprehensive study of optical solitons supported by spiral potentials in media with the cubic-quintic (CQ) nonlinearity. A variety of families of stationary states, including fundamental and high-order (excited) in-phase, out-of-phase, and hybrid-phase ones, are found. The linear stability analysis, corroborated by direct simulations, demonstrates that all upper-branch nonlinear states in potentials with different azimuthal indices are \emph{completely stable}, which rarely occurs in soliton physics. Our findings suggest spiral potentials as an effective means for multistable optical trapping, with potential applications in all-optical data processing.

nlin.PS↗

arXiv2026

Anomalous Topological Bloch Oscillations under Non-Abelian Gauge Fields

Topological Bloch oscillations are a hallmark of quantum transport phenomenon in which wavepackets undergo oscillatory motion driven by the interplay between an external force and topological edge states and serve as a powerful dynamical probe for the geometric properties of topological bands. Spin-orbit coupling (SOC) has also emerged as a crucial ingredient for manipulating quantum states in materials, with the corresponding gauge fields arising from the Rashba and Dresselhaus interactions. In this work, we investigate the propagation of spinor wavepackets in a honeycomb Zeeman lattice governed by the Gross-Pitaevskii equation. By tuning the relative strengths of Rashba and Dresselhaus SOC, we engineer a non-Abelian gauge field that drives anomalous topological Bloch oscillations (ATBOs). Unlike conventional topological Bloch oscillation (TBOs), these ATBOs exhibit asymmetric motion, including a freezing effect in one half of the oscillation cycle, which can be tuned by the SOC parameters and external forces. Our findings establish SOC-based non-Abelian gauge fields as a powerful mechanism controlling topological quantum dynamics, with implications for spintronic devices and quantum data processing.

cond-mat.quant-gas↗

arXiv2026

Multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials

We address the existence, stability, and dynamics of single-ring and multi-ring vorticity-carrying necklace solitons under the action of the Kerr nonlinearity and a Bessel-lattice potential modulated in the azimuthal direction. The model may be realized in the spatial domain for bulk optical waveguides, the spatiotemporal domain for optical cavities, and for effectively two-dimensional Bose-Einstein condensates. The setup supports single- and multi-ring necklace vortex patterns, including monopoles, dipoles, tripoles, quadrupoles, pentapoles, sextupoles, octupoles, and 12-poles. In contrast with the inherent instability of conventional vortex beams with high topological charges (winding numbers), vortex necklace-shaped solitons with large winding numbers are found to be stable in the present setup. In particular, octupoles exhibit stable breathing dynamics, and 12-pole necklaces with high winding numbers may be stable. These findings provide a new way for generating stable vortex necklaces, offering a vast potential for manipulations of complex spatiotemporal light fields.

physics.optics↗

arXiv2026

Flat-top solitons and anomalous interactions in media with even-order dispersions and competing nonlinearities

Flat-top (FT) solitons are optical pulses that arise from the balance of dispersion and self-phase modulation in media with the competing cubic-quintic nonlinearity. Previously, FT solitons were studied only in the case of the second-order dispersion ($m=2$). Following the recent observation of pure-quartic solitons (corresponding to $m=4$), we here construct families of FT solitons in the setting with pure-high-even-order dispersion (PHEOD), including $m=4,6,8$, and $10$, and address interactions between them. The PHEOD solitons are completely stable, and, unlike the conventional solitons, they feature oscillatory tails. Interactions between the PHEOD solitons are anomalous, featuring repulsion and attraction between in- and out-of-phase solitons, respectively. These results expand the variety of optical solitons maintained by diverse dispersive nonlinear media.

physics.optics↗

arXiv2026

Toroidal Confinement and Beyond: Vorticity-Defined Morphologies of Dipolar $^{164}$Dy Quantum Droplets

We investigate the formation, stability, and dynamics of 3D ring-shaped and multipole vortical quantum droplets (QDs) in non-rotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDI) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity $S$) are shaped as necklace-like modes, with the number of \textquotedblleft beads" (multipole's order) $n=2S$, up to $S=6$. The stability area of the multipoles shrinks with the increase of $S$. For higher values of $S$ the centrifugal effect associated with the phase winding destabilizes the annular density and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy and peak density on the norm (number of particles) and $S$ is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the non-rotating configurations.

cond-mat.quant-gas↗

arXiv2026

Nonlinear quadrupole topological insulators

Higher-order topological insulators (HOTIs) represent a family of topological phases that go beyond the conventional bulkboundary correspondence. d-dimensional n-th order HOTIs maintain (d - n)-dimensional gapless boundary states (in particular, zero-dimensional corner states in the case of d = n = 2). HOTIs of the Wannier type cam be extended into the nonlinear regime. Another prominent class of HOTIs, in the form of multipole insulators, was investigated only in the linear regime, due to the challenge of simultaneously achieving both negative hopping and strong nonlinearity. Here we propose the concept of nonlinear quadrupole topological insulators (NLQTIs) and report their experimental realization in an electric circuit lattice. Quench-initiated dynamics gives rise to nonlinear topological corner states and topologically trivial corner solitons, in weakly and strongly nonlinear regimes, respectively. Furthermore, we reveal the formation of two distinct types of bulk solitons, one existing in the middle finite gap under the action of weak nonlinearity, and another one found in the semi-infinite gap under strong nonlinearity. This work realizes another member of the nonlinear HOTI family, suggesting directions for exploring novel solitons across a broad range of topological insulators.

physics.optics↗

arXiv2026

Physics-Informed Neural Networks for the Quantum Droplets in Binary Bose-Einstein Condensates

Physics-Informed Neural Networks (PINNs), which integrate deep learning with physical prior knowledge, have proven to be a powerful tool for studying the dynamics of high-dimensional nonlinear systems. The present work utilizes PINNs to analyze the existence and evolution of quantum droplets (QDs) in a binary Bose-Einstein condensate (BEC), revealing the ability of this technique to accurately predict structural features of the QDs, their multipeak profiles, and dynamical behavior. The stable evolution of multipole QDs is thus demonstrated. Comparing different network architectures, including the training time, loss values, and $\mathbb{L_{2}}$ error, PINNs accurately predict specific dynamical characteristics of QDs. Furthermore, the PINN robustness is evaluated by the application of PINN to parameter-discovery tasks, considering both clean training data and data contaminated by $1\%$ random noise. The results highlight the efficiency of PINNs in modeling complex quantum systems and extracting reliable parameters under the noisy conditions.

cond-mat.quant-gas↗

arXiv2026

Gap solitons of the Wannier and Bloch types in spin-orbit-coupled Bose-Einstein condensates with a moiré lattice

Gap solitons (GSs) bifurcating from flat bands, which may be represented in terms of Wannier functions, have garnered significant interest due to their strong localization with extremely small norms. Moiré lattices (MLs), with multiple flat bands, offer an appropriate platform for creating such solitons. We explore the formation mechanism and stability of GSs in spin-1 Bose-Einstein condensates under the combined action of the Rashba spin-orbit coupling (SOC) and an ML potential. We identify five Wannier-type GS families bifurcating from the lowest five energy bands in the spectrum induced by the ML with sufficiently large period and depth. These fundamental GSs serve as basic elements for constructing more complex Wannier-type GS states. Reducing the lattice period and depth triggers a transition from the Wannier-type GSs to ones of the Bloch type, the latter exhibiting higher norm thresholds and pronounced spatial broadening near edges of the energy bands. In addition to tuning the lattice-potential parameters, adjusting the SOC strength can also modulate the flatness of energy bands and enhance the localization of gap solitons, enabling reversible transitions between the GSs of the Wannier and Bloch types. Distinctive properties of GSs in the quasiperiodic ML are uncovered too. Thus, we propose the theoretical foundation for the creation of and manipulations with strongly localized GSs.

cond-mat.quant-gas↗

arXiv2026

Dynamical correlations and chimera-like states of nanoemitters coupled to plasmon-polaritons in a lattice of conducting nanorings

We systematically investigate semiclassical dynamics of the optical field produced by quantum nanoemitters (NEs) embedded in a periodic lattice of conducting nanorings (NRs), in which plasmon polaritons (PPs) are excited. The coupling between PPs and NEs through the radiated optical field leads to establishment of a significant cross-correlation between NEs, so that their internal dynamics (photocurrent affected by the laser irradiation) depends on the NR's plasma frequency $ω_{p}$. The transition to this regime,combined with the nonlinearity of the system, leads to a steep increase of the photocurrent in the NEs, as well as to non-smooth (chimera-like or chaotic) behavior in the critical (transition) region, where small variations of $ω_{p}$ lead to significant changes in the level of the NE pairwise cross-correlations. The chimera-like state is realized as coexistence of locally synchronized and desynchronized NE dynamical states. A fit of the dependence of the critical current on $ω_{p}$ is found, being in agreement with results of numerical simulations. The critical effect may help to design new optical devices, using dispersive nanolattices which are made available by modern nanoelectronics.

physics.optics↗

arXiv2026

Collisions and fusion of one- and two-dimensional solitons driven by potential troughs in the cubic-quintic nonlinear Schrödinger equations

We study the formation and collision of one- and two-dimensional (1D and 2D) Gaussian-shaped and flat-top (FT) solitons in the framework of the nonlinear Schrödinger equation with the cubic-quintic nonlinearity and two intersecting potential troughs. We find that Gaussian-Gaussian and Gaussian-FT collisions between the solitons, steered by the troughs, are quasi-elastic, while the collisions between FT solitons may be either quasi-elastic or inelastic, in the form of merger into a single FT soliton, thus spontaneously breaking the symmetry between the steering troughs. The Gaussian-FT collisions, being overall quasi-elastic, generate weak radiation fields.

nlin.PS↗

arXiv2025

Guided vortex bullets

By means of the variational method and numerical simulations, we demonstrate the existence of stable 3D nonlinear modes, viz. vortex ``bullets'', in the form of pulsed beams carrying orbital angular momentum, that can self-trap in a 2D waveguiding structure. Despite the attractive self-interaction, which is necessary for producing the bullets (bright solitons), and which readily leads to the collapse in the 3D setting as well as to spontaneous splitting of vortex modes, we find a critical value of the trapping depth securing the stabilization of the vortex bullets. We identify experimental conditions for the creation of these topological modes in the context of coherent optical and matter waves. Collisions between the bullets moving in the unconfined direction are found to be elastic. These findings contribute to the understanding of self-trapping in nonlinear multidimensional systems and suggest new possibilities for the stabilization and control of 3D topological solitons.

physics.optics↗

arXiv2025

Intracavity-birefringence-enabled soliton states and wavelength control in the (C + L)-band fiber lasers

We demonstrate a compact all-fiber nonlinear-polarization-evolution (NPE) fiber laser capable of outputting wavelength-manipulated multiple laser states in the C + L band. Leveraging the intracavity birefringence-induced filtering effect, without external spectral filters, the laser achieves wavelength-tunable conventional solitons (CSs) and soliton molecules (SMs) with a tuning range of 72.85 nm and 45.54 nm, respectively, by adjusting the polarization states and pump power. Furthermore, wavelength-switchable harmonic mode-locking (over 1 GHz) and dual-wavelength mode-locking can also be achieved in the C + L band. To the best of our knowledge, this is the first experimental realization of wavelength-manipulated multiple soliton states covering the C + L band in a single-fiber-laser oscillator. Two examples of digital multi-letter encoding and transmission are further demonstrated on this platform by means of pump-driven wavelength/soliton states switching. By enabling controllable multi-state solitons and broad spectral tunability within a compact architecture, our work provides a promising source for spectrally diverse and temporally stable pulsed light sources that hold significant promise for applications in microscopy, bioimaging, and LiDAR.

physics.optics↗

arXiv2025

Quasi-confined modes produced by the Lugiato-Lefever model with a localized pump and the pseudo-Raman term

We introduce an extended nonlinear Lugiato-Lefever equation (LLE) with the pseudo-stimulated-Raman-scattering (pseudo-SRS) cubic term, linear damping/gain, and spatial inhomogeneous (weakly or strongly localized) pump. The LLE is derived, in the extended adiabatic approximation, from the underlying Zakharov system (ZS), which includes a viscosity term, acting on its low-frequency (LF) component, and the pump supporting the high-frequency (HF) one. Dynamics of quasi-solitons in the model is addressed by means of analytical and numerical methods. The sech-based approximation for the quasi-soliton predicts it as a stable fixed point (FP) of the system of evolution equations for the moments of the system moments (the HF norm, wave momentum, and center-of-mass coordinate). The attraction basin of the FP is identified too. The prediction is corroborated by direct simulations of the full LLE. A quasi-singular mode, supported by the delta-functional pump, is briefly considered too.

nlin.PS↗

arXiv2025

Robust quantum-droplet necklace clusters in three dimensions

We report the existence of quasi-stable ring-shaped (necklace-shaped) clusters built, in the free space, of 3D quantum droplets (QDs) in a binary Bose-Einstein condensate, modeled by the Gross-Pitaevskii equations with the Lee-Huang-Yang corrections. The QD clusters exhibit diverse dynamical behaviors, including contraction, oscillations, and expansion, depending on the cluster's initial radius. A phase shift between adjacent QDs imparts net angular momentum to the cluster, inducing its permanent rotation. Through the energy-minimization analysis, we predict equilibrium values of the necklace radius that support persistent rotation with negligible radial pulsations. In this regime, the clusters evolve as robust entities, maintaining the azimuthal symmetry in the course of the evolution, even in the presence of considerable perturbations. Necklace "supervortex" clusters, composed of QDs with inner vorticity 1 and global vorticity M, imprinted onto the cluster, may also persist for a long time. The reported findings may facilitate the experimental realization of complex self-sustained quantum states in the 3D free space.

cond-mat.quant-gas↗