arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 55 records · Page 3Linked to original sources

arXiv2025

Stable multipole solitons in defocusing saturable media with an annular trapping potential

We systematically investigate the existence, stability, and propagation dynamics of multipole-mode (necklace-shaped) solitons in the two-dimensional model of an optical medium with the defocusing saturable nonlinearity and an annular potential trough. Various families of stable multipole solitons trapped in the trough, from dipole, quadrupole, and octupole ones to multi-lobe complexes, are found. The existence domain remains invariant with the increase of the potential's depth. Solitons with a large number N of lobes are stable in a wide parameter region, up to N=48 and even farther. Actually, stable multipole solitons of an arbitrarily high order N can be found, provided that the trough's radius is big enough. The power of stable multipoles is essentially larger in comparison to previously studied models. It is demonstrated analytically and numerically that the application of a phase torque initiates stable rotation of the multipole complexes. Thus, we put forward an effective scheme for the stabilization of multipole solitons with an arbitrary high number of lobes, including rotating ones, which offers new possibilities for manipulating complex light beams.

nlin.PS↗

arXiv2025

An amended Ehrenfest theorem for the Gross-Pitaevskii equation in one- and two-dimensional potential boxes

It is known that the usual form of the Ehrenfest theorem (ET), which couples the motion of the center of mass (COM) of the one-dimensional (1D) wave function to the respective classical equation of motion, is not valid in the case of the potential box, confined by the zero boundary conditions. A modified form of the ET was proposed for this case, which includes an effective force originating from the interaction of the 1D quantum particle with the box edges. In this work, we derive an amended ET for the Gross-Pitaevskii equation (GPE), which includes the cubic nonlinear term, as well as for the 2D square-shaped potential box. In the latter case, we derive an amended COM equation of motion with an effective force exerted by the edges of the rectangular box, while the nonlinear term makes no direct contribution to the 1D and 2D versions of the ET. Nonetheless, the nonlinearity affects the amended ET through the edge-generated force. As a result, the nonlinearity of the underlying GPE can make the COM motion in the potential box irregular. The validity of the amended ET for the 1D and 2D GPEs with the respective potential boxes is confirmed by the comparison of numerical simulations of the underlying GPE and the corresponding amended COM equation of motion. The reported findings are relevant to the ongoing experiments carried out for atomic Bose-Einstein condensates trapped in the box potentials.

cond-mat.quant-gas↗

arXiv2025

Hopfions in the Lee-Huang-Yang superfluids

It is known that, under appropriate conditions, mean-field interactions can be canceled in binary BEC, leading to the formation of the Lee-Huang-Yang (LHY) superfluid, in which the nonlinearity is solely represented by the quartic LHY term. In this work we systematically investigate the existence, stability and evolution of hopfion states in this species of quantum matter. They are characterized by two independent topological winding numbers: inner twist $s$ of the vortex-ring core and overall vorticity $m$. The interplay between the LHY self-repulsion and a trapping harmonic-oscillator potential results in stability of the hopfions with $s = 1$ and $m$ ranging from $0$ to $4$. The hopfions exhibit distinct topological phase distributions along the vertical axis and the radial direction in the horizontal plane. Their effective radius and peak density increase with the chemical potential, along with expansion of the vortex-ring core. Although the instability domain of the hopfion modes broadens with the increase of $m$, stable hopfions persist in a wide range of the chemical potential, up to $m=4$, at least, provided that the norm exceeds a certain threshold value. The predictions are experimentally accessible in currently used BEC setups.

cond-mat.quant-gas↗

arXiv2025

Multidimensional Soliton Systems: an Update

A briefly formulated update of the recently published review [1] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose-Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple quantum droplets in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and fractional diffraction, and the prediction of stable 3D vortex solitons in various BEC schemes with long-range interactions.

nlin.PS↗

arXiv2025

Multi-Soliton Propagation and Interaction in $Λ$-Type EIT Media: An Integrable Approach

Electromagnetically induced transparency (EIT) is well known as a quantum optical phenomenon that permits a normally opaque medium to become transparent due to the quantum interference between transition pathways. This work addresses multi-soliton dynamics in an EIT system modeled by the integrable Maxwell-Bloch (MB) equations for a three-level $Λ$-type atomic configuration. By employing a generalized gauge transformation, we systematically construct explicit N-soliton solutions from the corresponding Lax pair. Explicit forms of one-, two-, three-, and four-soliton solutions are derived and analyzed. The resulting pulse structures reveal various nonlinear phenomena, such as temporal asymmetry, energy trapping, and soliton interactions. They also highlight coherent propagation, elastic collisions, and partial storage of pulses, which have potential implications for the design of quantum memory, slow light and photonic data transport in EIT media. In addition, the conservation of fundamental physical quantities, such as the excitation norm and Hamiltonian, is used to provide direct evidence of the integrability and stability of the constructed soliton solutions.

nlin.PS↗

arXiv2025

Breather gas and shielding for the focusing nonlinear Schrödinger equation with nonzero backgrounds

Breathers have been experimentally and theoretically found in many physical systems -- in particular, in integrable nonlinear-wave models. A relevant problem is to study the \textit{breather gas}, which is the limit, for $N\rightarrow \infty $, of $N$-breather solutions. In this paper, we investigate the breather gas in the framework of the focusing nonlinear Schrödinger (NLS) equation with nonzero boundary conditions, using the inverse scattering transform and Riemann-Hilbert problem. We address aggregate states in the form of $N$-breather solutions, when the respective discrete spectra are concentrated in specific domains. We show that the breather gas coagulates into a single-breather solution whose spectral eigenvalue is located at the center of the circle domain, and a multi-breather solution for the higher-degree quadrature concentration domain. These coagulation phenomena in the breather gas are called \textit{breather shielding}. In particular, when the nonzero boundary conditions vanish, the breather gas reduces to an $n$-soliton solution. When the discrete eigenvalues are concentrated on a line, we derive the corresponding Riemann-Hilbert problem. When the discrete spectrum is uniformly distributed within an ellipse, it is equivalent to the case of the line domain. These results may be useful to design experiments with breathers in physical settings.

nlin.SI↗

arXiv2025

One- and two-dimensional solitons under the action of the inverted cubic-quintic nonlinearity

The usual cubic-quintic (CQ) nonlinearity is proved to sustain one- and two-dimensional (1D and 2D) broad (flat-top) solitons. In this work, we demonstrate that 1D and 2D soliton families can be supported, in the semi-infinite bandgap (SIBG), by the interplay of a lattice potential and the nonlinearity including self-defocusing cubic and self-focusing quintic terms, with the sign combination inverted with respect to the usual CQ nonlinearity. The families include fundamental and dipole solitons in 1D, and fundamental, quadrupole, and vortex solitons in 2D. The power, shapes, and stability of the solitons are reported. The results are strongly affected by the positions of the solitons in SIBG, the families being unstable very close to or very far from the SIBG's edge. The inverted CQ nonlinearity, considered in this work, sustains sharp 1D and 2D stable solitons, which can be naturally used as bit pixels in photonic data-processing applications.

nlin.PS↗

arXiv2025

A fiber-loop laser with a cooled erbium-doped section

An optical comb featuring an unusual structure has been recently observed in a fiber-loop laser running at cryogenic temperatures. In the present work, the effect of optical polarization on the operation of the laser is explored. Multi--mode lasing with a relatively high degree of inter--mode coherency is experimentally demonstrated. The setup can be used for applications to spectroscopy, communications, and quantum data storage.

physics.optics↗

arXiv2025

Transformation of topological optical states via spiral modulation in fractional-diffraction systems

We propose a scheme for manipulations of a variety of topological states in fractional optical systems through spiral modulation of the local refraction index. An analytical approximation, based on a truncated finite-mode system, and direct simulations reveal that the spiral modulation supports direct mutual conversion between eigenmodes with topological-charge difference Δm=1, driven by the resonant coupling between the modes and the underlying spiral modulation. The conversion between eigenmodes with Δm=2 requires involvement of an intermediary mode and precise tuning of the resonance condition. We further explore the conversion of degenerate modes under the action of azimuthal modulation. Modulated degenerate modes exhibit incomplete conversion, evolving into intermediate states with odd parity symmetry. Finally, we examine nonlinear effects on the spiral-modulation-induced mode conversion, identifying an essential nonlinearity-induced resonance-frequency shift that critically affects the conversion efficiency.

physics.optics↗

arXiv2025

Phase transitions and dynamics of one-dimensional solitons in spin-orbit-coupled Bose-Bose mixtures

We investigate the formation, stability, and dynamics of solitons in a one-dimensional binary Bose-Einstein condensate under the action of the spin-orbit-coupling (SOC) and Lee-Huang-Yang (LHY) correction to the underlying system of the Gross-Pitaevskii equations. We identify the semi-dipole (SD) family of solitons and thoroughly analyze its properties. The numerical analysis reveals intricate bifurcations, including transitions from real to complex-valued stationary wavefunctions of the SD solitons and norm-dependent dynamical instabilities. Stability maps in the plane of the solitons' norm and interaction strength exhibit areas of monostability, oscillatory behavior, and soliton splitting. Solitons with complex stationary wavefunctions emerge as ground states in broad parameter areas, due to the effects of the LHY terms. The other soliton species, in the form of mixed modes (MMs), does not feature the compexification bifurcation. In the LHY-dominated regime, the SD and MM solitons exhibit identical values of the energy for the same norm. The results deepen the understanding of nonlinear matter-wave states and reveal multi-stable ones in quantum gases.

cond-mat.quant-gas↗

arXiv2025

Multipulse Soliton Attractors Facilitated by High-Birefringence Fibers

The stability of optical solitons is a crucial factor in various applications. This work reveals a novel stable multipulse soliton attractor in fiber lasers. The attractor represents a bound state of multiple solitons, pulling other dynamical states toward itself. By introducing a polarization-maintaining fiber (PMF), the enhanced birefringence in the cavity induces the differential group delay (DGD) between the polarization components of the pulse, leading to soliton splitting and, ultimately, the formation of multi-soliton states. These multi-solitons, affected by intracavity nonlinear and dissipative effects, form attractors consisting of one to seven soliton pulses. Through a combination of experiments and numerical simulations, we systematically investigate the robustness and dynamical behavior of the multipulse soliton attractors. In this context, we analyze disturbances introduced by "rogue" solitons with different frequencies and conduct a comprehensive study of their interaction with the multipulse soliton attractors. The results show that the multipulse soliton attractors are structurally stable and highly resistant to external disturbances, highlighting their potential for high-precision fiber lasers and advanced multipulse systems.

physics.optics↗

arXiv2025

Observation of edge solitons and transitions between them in a trimer circuit lattice

In nonlinear topological systems, edge solitons either originate from linear topological edge modes or emerge as nonlinearity-induced localized states without topological protection. While electric circuits (ECs) provide a platform for realizing various types of topological insulators, observation of edge solitons and transitions between them in EC lattices remains a challenging problem. Here, we realize quench dynamics in nonlinear ECs to experimentally demonstrate both topologically nontrivial and trivial edge solitons in a trimer EC lattice and transitions between them. In the weakly nonlinear regime, we observe two types of topologically nontrivial edge solitons that originate from the corresponding linear topological edge states, characterized by the presence of mutually antisymmetric or symmetric peaks at two edge sites. Under strong nonlinearity, topologically trivial edge solitons with antisymmetric, symmetric, and asymmetric internal structures are discovered. The work suggests possibilities for exploring sophisticated nonlinear states and transitions between them in nonlinear topological systems.

nlin.PS↗

arXiv2025

Controlled Fission and Superposition of Vector Solitons in an Integrable Model of Two-Component Bose-Einstein Condensates

We investigate the dynamics of vector solitons in a two-component Bose-Einstein condensates governed by the system of Gross-Pitaevskii equations. Using a gauge-transformation approach, we construct a four-soliton solution and analyze their interactions, including superposition states, fission, and shape-preserving collisions. We explore the ability of time-dependent parameters, such as the intra- and intercomponent interaction coefficients and trapping potential, to control the soliton properties. In particular, we demonstrate controlled four-soliton fission, highlighting its potential applications to quantum data processing and coherent matter-wave transport. The results suggest experimental realization in BEC systems and provide insights into nonlinear wave interactions in multicomponent quantum fluids.

nlin.PS↗

arXiv2025

Spontaneous symmetry breaking in continuous waves, dark solitons, and vortices in linearly coupled bimodal systems

We introduce a model governing the copropagation of two components which represent circular polarizations of light in the optical fiber with relative strength g = 2 of the nonlinear repulsion between the components, and linear coupling between them. A more general system of coupled Gross-Pitaevskii (GP) equations, with g =/= 2 and the linear mixing between the components, is considered too. The latter system is introduced in its one- and two-dimensional (1D and 2D) forms. A new finding is the spontaneous symmetry breaking (SSB) of bimodal CW (continuous-wave) states in the case of g > 1 (in the absence of the linear coupling, it corresponds to the immiscibility of the nonlinearly interacting components). The SSB is represented by an exact asymmetric CW solution. An exact solution is also found, in the case of g = 3, for stable dark solitons (DSs) supported by the asymmetric CW background. For g =/= 3, numerical solutions are produced for stable DSs supported by the same background. Moreover, we identify a parameter domain where the fully miscible (symmetric) CW background maintains stable DSs with the inner SSB (separation between the components) in its core. In 2D, the GP system produces stable vortex states with a shift between the components and broken isotropy. The vortices include ones with the inter-component shift imposed by the asymmetric CW background, and states supported by the symmetric background, in which the intrinsic shift (splitting) is exhibited by vortical cores of the two components.

nlin.PS↗

arXiv2025

Stable hopfions in trapped quantum droplets

Hopfions are a class of three-dimensional (3D) solitons which are built as vortex tori carrying intrinsic twist of the toroidal core. They are characterized by two independent topological charges, \textit{viz}., vorticity $S$ and winding number $M$ of the intrinsic twist, whose product determines the \textit{Hopf number}, $Q_{H}=MS$, which is the basic characteristic of the hopfions. We construct hopfions as solutions of the 3D Gross-Pitaevskii equations (GPEs) for Bose-Einstein condensates in binary atomic gases. The GPE system includes the cubic mean-field self-attraction, competing with the quartic self-repulsive Lee-Huang-Yang (LHY) term, which represents effects of quantum fluctuations around the mean-field state, and a trapping toroidal potential (TP). A systematic numerical analysis demonstrates that families of the states with $S=1,M=0$, i.e., $Q_{H}=0$, are stable, provided that the inner TP\ radius $R_{0}$ exceeds a critical value. Furthermore, true hopfions with $S=1,M=1\sim 7$, which correspond, accordingly, to $Q_{H}=1\sim 7$, also form partly stable families, including the case of the LHY\ superfluid, in which the nonlinearity is represented solely by the LHY term. On the other hand, the hopfion family is completely unstable in the absence of the LHY term, when only the mean-field nonlinearity is present. We illustrate the knot-like structure of the hopfions by means of an elementary geometric picture. For $Q_{H}=0$, circles which represent the \textit{preimage} of the full state do not intersect. On the contrary, for $Q_{H}\geq 1$ they intersect at points whose number is identical to $Q_{H}$. The intersecting curves form multi-petal structures with the number of petals also equal to $Q_{H}$.

cond-mat.quant-gas↗

arXiv2025

Tightly bound solitons and vortices in three-dimensional bosonic condensates with the electromagnetically-induced gravity

The $1/r$ long-range interaction, induced by laser illumination, offers a mechanism for the implementation of stable self-trapping in Bose-Einstein condensates (BECs) in the three-dimensional free space. Using the variational approximation and numerical solutions, we find that self-trapped states in this setting , with attractive nonlocal and repulsive local interactions, resemble tightly-bound compactons. However, these are not true compactons but rather \textit{tightly self-trapped modes} (TSTMs), with small-amplitude nonvanishing tails. The structure of the self-trapped states is explained by an analytical solution for their tails. Further, we demonstrate that stable % TSTMs with embedded vorticity, exist in the same setting, with winding numbers up to $S=6$ (at least). Addressing two-TSTM interactions, we find that pairs of ground states (GSs, with $S=0$), as well as vortex-vortex and vortex-antivortex pairs (with $S_1=S_2$ and $S_1=-S_2$, respectively), form stably rotating bound states. Head-on collisions between vortex TSTMs, set in slow motion by kicks, are inelastic, resulting in their merger into a GS soliton, that may either remain at the collision position or move aside, shedding the angular momentum with emitted radiation, or, alternatively, lead to the formation of a vortex that also moves aside.

cond-mat.quant-gas↗

arXiv2025

Elongated vortex quantum droplets in binary Bose-Einstein condensates

Stability of elongated (``slender") quantum droplets (QDs) with embedded unitary and multiple vorticity is a problem that was not solved previously. In this work, we propose a solution which relies upon the use of the spatial modulation of the inter-species scattering length in the binary Bose-Einstein condensates, in the form of a two-dimensional axisymmetric Gaussian, shaped by means of the optical Feshbach resonance. The corresponding effective nonlinear trapping potential supports completely stable elongated QDs with vorticity $S=0$ and partly stable families of elongated QDs with $S=1,2,3,4$ (other nonlinear systems do not maintain stability of vortex droplets with $\geq 2$). We systematically analyze effects of the amplitude and width of the Gaussian modulation, as well as the total number of atoms, on the shape and stability of the QDs, some effects being explained analytically. Collisions between identical QDs with $% S=1$ moving in opposite directions along the central axis leads to their merger into still more elongated breathing QDs with the same vorticity, while collisions between QDs with $S=\pm 1$ are quasi-elastic. Moving modulation profiles are able to adiabatically rotate the trapped elongated QDs. Application of a torque to the vector QD sets in the gyroscopic regime of robust precession, which realizes a macroscopic spin-orbit-coupling effect.

cond-mat.quant-gas↗

arXiv2025

Spontaneous symmetry and antisymmetry breaking in a ring with two potential barriers

We propose a fundamental setup for the realization of spontaneous symmetry breaking (SSB) and spontaneous antisymmetry breaking (SASB) in the framework of the nonlinear Schroedinger equation with the self-attractive and repulsive cubic term, respectively, on a one-dimensional ring split in two mutually symmetric boxes by delta-functional potential barriers, placed at opposite points. The system is relevant to optics and BEC. The spectrum of the linearized system is found in analytical and numerical forms. SSB and SASB are predicted by dint of the variational approximation, and studied in the numerical form. A particular stable solution, which demonstrates strong asymmetry, is found in an exact form. In the system with the attractive nonlinearity, the SSB of the symmetric ground state is initiated by the modulational instability. It creates stationary asymmetric states through a supercritical bifurcation. In the self-repulsive system, SASB makes the lowest antisymmetric excited state unstable, transforming it into an antisymmetry-breaking oscillatory mode.

nlin.PS↗