arXiv subjects

Liangwei Zeng

Publications and source records attributed to Liangwei Zeng.

17 recordsLinked to original sources

arXiv2026

Collisions and fusion of one- and two-dimensional solitons driven by potential troughs in the cubic-quintic nonlinear Schr\"{o}dinger 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 Schr\"{o}dinger 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

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↗

arXiv2024

Solitons in composite linear-nonlinear moir\'{e} lattices

We produce families of two-dimensional gap solitons (GSs) maintained by moir\'{e} lattices (MLs) composed of linear and nonlinear sublattices, with the defocusing sign of the nonlinearity. Depending on the angle between the sublattices, the ML may be quasiperiodic or periodic, composed of mutually incommensurate or commensurate sublattices, respectively (in the latter case, the inter-lattice angle corresponds to Pythagorean triples). The GSs include fundamental, quadrupole, and octupole solitons, as well as quadrupoles and octupoles carrying unitary vorticity. Stability segments of the GS families are identified by means of the linearized equation for small perturbations, and confirmed by direct simulations of perturbed evolution.

physics.optics↗

arXiv2023

A solvable model for symmetry-breaking phase transitions

Analytically solvable models are benchmarks in studies of phase transitions and pattern-forming bifurcations. Such models are known for phase transitions of the second kind in uniform media, but not for localized states (solitons), as integrable equations which produce solitons do not admit intrinsic transitions in them. We introduce a solvable model for symmetry-breaking phase transitions of both the first and second kinds (alias sub- and supercritical bifurcations) for solitons pinned to a combined linear-nonlinear double-well potential, represented by a symmetric pair of delta-functions. Both self-focusing and defocusing signs of the nonlinearity are considered. In the former case, exact solutions are produced for symmetric and asymmetric solitons. The solutions explicitly demonstrate a switch between the symmetry-breaking transitions of the first and second kinds (i.e., sub- and supercritical bifurcations, respectively). In the self-defocusing model, the solution demonstrates the transition of the second kind which breaks antisymmetry of the first excited state.

nlin.PS↗

arXiv2023

Second-harmonic generation in the system with fractional diffraction

We construct a family of bright optical solitons composed of fundamental frequency (FF) and second-harmonic (SH) components in the one-dimensional (planar) waveguide with the quadratic (second-harmonic-generating) nonlinearity and effective fractional diffraction, characterized by the Levy index α, taking values between 2 and 0.5, which correspond to the non-fractional diffraction and critical collapse, respectively. The existence domain and stability boundary for the solitons are delineated in the space of α, FF-SH mismatch parameter, and propagation constant. The stability boundary is tantamount to that predicted by the Vakhitov-Kolokolov criterion, while unstable solitons spontaneously evolve into localized breathers. A sufficiently weak transverse kick applied to the stable solitons excite small internal vibrations in the stable solitons, without setting them in motion. A stronger kick makes the solitons' trajectories tilted, simultaneously destabilizing the solitons.

nlin.PS↗

arXiv2021

Quadratic fractional solitons

We introduce a system combining the quadratic self-attractive or composite quadratic-cubic nonlinearity, acting in the combination with the fractional diffraction, which is characterized by its Lévy index $α$. The model applies to a gas of quantum particles moving by Lévy flights, with the quadratic term representing the Lee-Huang-Yang correction to the mean-field interactions. A family of fundamental solitons is constructed in a numerical form, while the dependence of its norm on the chemical potential characteristic is obtained in an exact analytical form. The family of \textit{quasi-Townes solitons}, appearing in the limit case of $α=1/2$, is investigated by means of a variational approximation. A nonlinear lattice, represented by spatially periodical modulation of the quadratic term, is briefly addressed too. The consideration of the interplay of competing quadratic (attractive) and cubic (repulsive) terms with a lattice potential reveals families of single-, double-, and triple-peak gap solitons (GSs) in two finite bandgaps. The competing nonlinearity gives rise to alternating regions of stability and instability of the GS, the stability intervals shrinking with the increase of the number of peaks in the GS.

cond-mat.quant-gas↗

arXiv2021

Single-shot framing integration photography with high spatial resolution at 5.3*1012 frames per second by an inversed 4f system

We present a framing integration ultrafast photography (FIP), which integrates the framing structure, codes a dynamic event by an inversed 4f system (I4F) and decodes regionally with high spatial resolution. In the experiment about laser-induced plasma, FIP achieved a framing rate of 5.3*1012 frames per second (fps) and an intrinsic spatial resolution of 110.4 lp/mm. It has an excellent spatio-temporal resolution and a compact and flexible structure. Hence, it can probe unrepeatable ultrafast intra- and inter-atomic/molecular dynamics, different in size and duration with high-quality. Besides, FIP can lay a foundation for integrating and simplifying ultrafast photography instruments. Here the minimum framing time (temporal resolution) is limited by only the laser pulse duration; be sure, attosecond laser technology may further increase framing rates by several orders of magnitude.

physics.optics↗

arXiv2021

Flat-floor bubbles, dark solitons, and vortices stabilized by inhomogeneous nonlinear media

We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in the form of flat-floor \textquotedblleft bubbles", and topological excitations, in the form of dark solitons in 1D and vortices with winding number $m$ in 2D. Unlike bright solitons, delocalized bubbles and dark modes were not previously considered in this setting. The ground and excited states are accurately approximated by the Thomas-Fermi expressions. The 1D and 2D bubbles, as well as vortices with $m=1$, are completely stable, while the dark solitons and vortices with $m=2$ have nontrivial stability boundaries in their existence areas. Unstable dark solitons are expelled to the periphery, while unstable double vortices split in rotating pairs of unitary ones. Displaced stable vortices precess around the central point.

nlin.PS↗

arXiv2021

Localized modes and dark solitons sustained by nonlinear defects

Dark solitons and localized defect modes against periodic backgrounds are considered in arrays of waveguides with defocusing Kerr nonlinearity constituting a nonlinear lattice. Bright defect modes are supported by local increase of the nonlinearity, while dark defect modes are supported by a local decrease of the nonlinearity. Dark solitons exist for both types of the defect, although in the case of weak nonlinearity they feature side bright humps making the total energy propagating through the system larger than the energy transferred by the constant background. All considered defect modes are found stable. Dark solitons are characterized by relatively narrow windows of stability. Interactions of unstable dark solitons with bright and dark modes are described.

nlin.PS↗

arXiv2021

Stable and oscillating solitons of $\mathcal{PT}$-symmetric couplers with gain and loss in fractional dimension

Families of coupled solitons of $\mathcal{PT}$-symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions modulation (CIM), are reported. Profiles, powers, stability areas, and propagation dynamics of the obtained $\mathcal{PT}$-symmetric coupled solitons are investigated. By comparing the results of the models with and without CIM, we find that the stability area of the model with CIM is much broader than the one without CIM. Remarkably, oscillating $\mathcal{PT}$-symmetric coupled solitons can also exist in the model of CIM with the same coefficients of the self- and cross-interactions modulations. In addition, the period of these oscillating coupled solitons can be controlled by the linear coupling coefficient.

nlin.PS↗

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↗

arXiv2019

One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential

Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and matter-wave media). A benign competition between self-focusing cubic and self-defocusing quintic nonlinear nonlinearities (known as cubic-quintic model) plays an important role in creating and stabilizing the self-trapping of D-dimensional localized structures, in the contexts of standard nonlinear Schrödinger equation. We incorporate an external periodic potential (linear lattice) into this model and extend it to the space-fractional scenario that begins to surface in very recent years---the nonlinear fractional Schrödinger equation (NLFSE), therefore obtaining the cubic-quintic or the purely quintic NLFSE, and investigate the propagation and stability properties of self-trapped modes therein. Two types of one-dimensional localized gap modes are found, including the fundamental and dipole-mode gap solitons. Employing the techniques based on the linear-stability analysis and direct numerical simulations, we get the stability regions of all the localized modes; and particularly, the anti-Vakhitov-Kolokolov criterion applies for the stable portions of soliton families generated in the frameworks of quintic-only nonlinearity and competing cubic-quintic nonlinear terms.

nlin.PS↗

arXiv2019

Gap-type dark localized modes in a Bose-Einstein condensate with optical lattices

Bose-Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years--particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes--gap solitons and soliton clusters--are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.

nlin.PS↗

arXiv2019

Gaussian-like and flat-top solitons of atoms with spatially modulated repulsive interactions

Solitons, nonlinear particle-like excitations with inalterable properties (amplitude, shape, and velocity) as they propagate, are omnipresent in many branches of science---and in physics in particular. Flat-top solitons are a novel type of bright solitons that have not been well explored in pure nonlinear media. Here, a model of nonlinear Kerr (cubic) media of ultracold atoms with spatially modulated repulsive interactions is proposed and shown to support a vast variety of stable flat-top matter-wave solitons, including one-dimensional (1D) flat-top fundamental and multipole solitons, two-dimensional (2D) flat-top fundamental and vortex solitons. We demonstrate that by varying the relevant physical parameters (nonlinearity coefficient and chemical potential) the ordinary bright (gaussian) solitons can transform into the novel flat-top solitons. The (in-)stability domains of the flat-top soliton families are checked by means of linear stability analysis and reconfirmed by direct numerical simulations. This model is generic in the contexts of nonlinear optics and Bose-Einstein condensates, which provide direct experimental access to observe the predicted solutions.

nlin.PS↗

arXiv2019

One-dimensional solitons in fractional Schrödinger equation with a spatially modulated nonlinearity: nonlinear lattice

The existence and stability of stable bright solitons in one-dimensional (1D) media with a spatially periodical modulated Kerr nonlinearity are demonstrated by means of the linear-stability analysis and in direct numerical simulations. The nonlinear potential landscape can balance the fractional-order diffraction and thus stabilizes the solitons, making the model unique and governed by the recently introduced fractional Schrödinger equation with a self-focusing cubic nonlinear lattice. Both 1D fundamental and multihump solitons (in forms of dipole and tripole ones) are found, which occupy one or three cells of the nonlinear lattice respectively, depending on the soliton's power (intensity). We find that the profiles of the predicted soliton families are impacted intensely by the Lévy index $α$ which denotes the level of fractional Laplacian, so does to their stability. The stabilization of soliton families is possible if $α$ exceeds a threshold value, below which the balance between fractional-order diffraction and the spatially modulated focusing nonlinearity will be broken.

nlin.PS↗

arXiv2019

A purely Kerr nonlinear model admitting flat-top solitons

We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including fundamental ones, 1D multipoles, and 2D vortices. Previously, solitons of this type were only produced by models with competing nonlinearities. The present setting may be implemented in optics and Bose-Einstein condensates. The 1D version gives rise to an exact analytical solution for stable flat-top solitons, and generic families may be predicted by means of the Thomas-Fermi approximation. Stability of the obtained flat-top solitons is analyzed by means of linear-stability analysis and direct simulations. Fundamental solitons and 1D multipoles with $k=1$ and $2$ nodes, as well as vortices with winding number $m=1$, are completely stable. For multipoles with $k\geq 3$ and vortices with $m\geq 2$, alternating stripes of stability and instability are identified in their parameter spaces.

physics.optics↗