Stability Of Solitons Research Articles

Dynamical self-trapping of two-dimensional binary solitons in cross-combined linear and nonlinear optical lattices.

Dynamical and self-trapping properties of two-dimensional (2D) binary mixtures of Bose-Einstein condensates in cross-combined lattices, consisting of a one-dimensional (1D) linear optical lattice (LOL) in the x direction for the first component and a 1D nonlinear optical lattice (NOL) in the y direction for the second component, are analytically and numerically investigated. The existence and stability of 2D binary matter wave solitons in these settings are demonstrated both by variational analysis and by direct numerical integration of the coupled Gross-Pitaevskii equations. We find that in the absence of the NOL, binary solitons, stabilized by the action of the 1D LOL and by the attractive intercomponent interaction, can freely move in the y direction. In the presence of the NOL, we find, quite remarkably, the existence of threshold curves in the parameter space separating regions where solitons can move from regions where the solitons become dynamically self-trapped. The mechanism underlying the dynamical self-trapping phenomenon (DSTP) is qualitatively understood in terms of a dynamical barrier induced by the NOL, similar to the Peirls-Nabarro barrier of solitons in discrete lattices. DSTP is numerically demonstrated for binary solitons that are put in motion both by phase imprinting and by the action of external potentials applied in the y direction. In the latter case, we show that the trapping action of the NOL allows one to maintain a 2D binary soliton at rest in a nonequilibrium position of a parabolic trap or to prevent it from falling under the action of gravity. Possible applications of the results are also briefly discussed.

Multi-peak solitons in parity-time symmetry composite Mathieu lattices

This paper numerically investigates the existence, stability, and transmission characteristics of multi-peak solitons in parity-time (PT) symmetric composite Mathieu lattices in self-focusing Kerr nonlinear media. These multi-peak solitons are highly sensitive to the incident light power, position, and phase. Different incident lights generate solitons with different transmission characteristics, especially the generation of breather soliton transmission characteristics. These findings have significant theoretical and practical implications for the fields of photonics and nonlinear optics.

Dynamical behavior of perturbed Gerdjikov–Ivanov equation through different techniques

The objective of this work is to investigate the perturbed Gerdjikov–Ivanov (GI) equation along spatio-temporal dispersion which explains the dynamics of soliton dispersion and evolution of propagation distance in optical fibers, photonic crystal fibers (PCF), and metamaterials. The algorithms, namely hyperbolic extended function method and generalized Kudryashov’s method, are constructed to obtain the new soliton solutions. The dark, bright, periodic, and singular solitons are derived of the considered equation with the appropriate choice of parameters. These results are novel, confirm the stability of optical solitons, and have not been studied earlier. The explanation of evaluated results is given by sketching the various graphs in 3D, contour and 2D plots by using Maple 18. Graphical simulations divulge that varying the wave velocity affects the dynamical behaviors of the model. In summary, this research adds to our knowledge on how the perturbed GI equation with spatio-temporal dispersion behaves. The obtained soliton solutions and the methods offer computational tools for further analysis in this field. This work represents an advancement in our understanding of soliton dynamics and their applications in photonic systems.

Stability and adaptive evolution of higher-order vector vortex solitons in thermally nonlinear media with tunable transverse size

The stability of a higher-order vector vortex (HVV) soliton, comprised of a fundamental-mode beam incoherently coupling with a higher-order vortex beam, is investigated in a thermally nonlocal nonlinear medium. By linear stability analysis, we find the broad and stable interval for HVV solitons and the monotonically increasing relation between the stable interval and the vortical topological charge. The adaptive evolution of this stable HVV soliton in the longitudinally-inhomogeneous medium with tunable transverse size is also discussed. The smooth transition and controllable propagation of HVV solitons, and the oscillating behaviour of HVV breathers under different nonlocal potentials are investigated. In addition, the instability suppression of the HVV soliton by means of gradual change of transverse size is also found.

Nonlinearity managed vector solitons

The evolution of vector solitons under nonlinearity management is studied. The averaged over strong and rapid modulations in time of the inter-species interactions vector Gross-Pitaevskii equation (GPE) is derived. The averaging gives the appearance of the effective nonlinear quantum pressure depending on the population of the other component. Using this system of equations, the existence and stability of the vector solitons under the action of the strong nonlinearity management (NM) is investigated. Using a variational approach the parameters of NM vector solitons are found. The numerical simulations of the full time-dependent coupled GPE confirm the theoretical predictions.

An artificial intelligence approach to design periodic nonlinear oscillator chains under external excitation with stable damped solitons

In this paper, an artificial intelligence approach is developed to create a metamodel of damped solitons in periodic nonlinear oscillator chains under external excitation. Unlike resonators subjected to parametric excitation, chains subjected exclusively to external excitation do not have known analytical solutions for Intrinsic Localized Modes (ILMs) when damping is pondered. The proposed metamodel is a quick design tool of nonlinear damped periodic structures describing effectively the behavior of solitonic solutions, demonstrating a computational cost considerably lower than that of the Newton method. The results of this work highlight the potential of ANN regression models in the description of physical phenomena represented by the Nonlinear Schrödinger Equation when damping is considered.

Unraveling the Dynamics of Singular Stochastic Solitons in Stochastic Fractional Kuramoto–Sivashinsky Equation

This work investigates the complex dynamics of the stochastic fractional Kuramoto–Sivashinsky equation (SFKSE) with conformable fractional derivatives. The research begins with the creation of singular stochastic soliton solutions utilizing the modified extended direct algebraic method (mEDAM). Comprehensive contour, 3D, and 2D visual representations clearly depict the categorization of these stochastic soliton solutions as kink waves or shock waves, offering a clear description of these soliton behaviors within the context of the SFKSE framework. The paper also illustrates the flexibility of the transformation-based approach mEDAM for investigating soliton occurrence not only in SFKSE but also in a wide range of nonlinear fractional partial differential equations (FPDEs). Furthermore, the analysis considers the effect of noise, specifically Brownian motion, on soliton solutions and wave dynamics, revealing the significant influence of randomness on the propagation, generation, and stability of soliton in complex stochastic systems and advancing our understanding of extreme behaviors in scientific and engineering domains.

Injection-locked soliton microcomb against temporal drifting

The soliton microcomb offers a unique and compact solution for photonics applications. However, the microcomb is suffering from the perturbations arising from complex higher-order effects such as self-steepening and third-order dispersion, leading to the temporal drift of soliton and the deviation of repetition rate. It is unfavorable to the stability in time and frequency domains. In this work, we numerically and theoretically demonstrate that the injection-locking scheme can effectively eliminate the soliton temporal drift and repetition rate deviation caused by complex higher-order effects. The mechanism of eliminating drift and deviation is explained, and the theoretically predicted stable soliton temporal position agrees well with the simulation. The modulation depth plays a key role in suppressing drift, and an experimental guide for adjusting modulation depth is given. This work enriches soliton dynamics under complex higher-order effects and provides a scheme to improve the stability and controllability of microcombs.

Binding dynamics of cavity solitons in a Kerr resonator with high order dispersion.

Cavity solitons are persistent light pulses arising from the externally driven Kerr resonators. Thanks to the passive parametric gain, cavity soliton has been endowed with the natural advantage of the chip-scaled integration since it was first experimentally generated in the fiber-based platform. Deterministic single soliton with smooth spectrum is a preferred state for numerous applications. However, multiple solitons are more common in the resonators with anomalous dispersion. In this condition, adjacent solitons are easily perturbed to attract and collide with each other. Some experimental observations deviated from the aforementioned description have recorded the stable soliton intervals that can last for a long time scale. This phenomenon is known as soliton binding and is attributed to the presence of narrow resonant sidebands in the spectrum. While the stationary configuration of two binding solitons has been investigated, the dynamical evolution remains an area for further exploration. In this paper, we discuss the binding dynamics of the cavity solitons in the presence of high-order dispersion. The proposed theoretical predictions match well with the numerical results, encompassing both the stationary stable intervals and dynamic trajectories. Our research will provide a comprehensive insight into the soliton motion induced by the internal perturbations.

Symmetry-breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials

We address symmetry-breaking bifurcations (SBBs) in the ground state (GS) and dipole-mode (DM) solitons of the one-dimensional linearly coupled NLS equations, modelling the propagation of light in a dual-core planar waveguide with the Kerr nonlinearity and two types of P T -symmetric potentials. The P T -symmetric potential is employed to obtain different types of solutions. A supercritical pitchfork bifurcation occurs in families of symmetric solutions of both the GS and DM types. A novel feature of the system is interplay between breakings of the P T and inter-core symmetries. Stability of symmetric GS and DM modes and their asymmetric counterparts, produced by SBBs of both types, is explored via the linear-stability analysis and simulations. It is found that the instability of P T -symmetric solutions takes place prior to the inter-core symmetry breaking. Surprisingly, stable inter-core-symmetric GS solutions may remain stable while the P T symmetry is broken. Fully asymmetric GS and DM solitons are only partially stable. Moreover, we construct symmetric and asymmetric GS solitons under the action of a pure imaginary localized potential, for which the SBB is subcritical. These results exhibit that stable solitons can still be found in dissipative systems. Finally, excitations of symmetric and asymmetric GS solitons are investigated by making the potential’s parameters or the system’s coupling constant functions, showing that GS solitons can be converted from an asymmetric shape onto a symmetric one under certain conditions. These results may pave the way for the study of linear and nonlinear phenomena in a dual-core planar waveguide with P T potential and related experimental designs.

Formation, propagation, and excitation of matter solitons and rogue waves in chiral BECs with a current nonlinearity trapped in external potentials.

In this paper, we investigate formation and propagation of matter solitons and rogue waves (RWs) in chiral Bose-Einstein condensates modulated by different external potentials, modeled by the chiral Gross-Pitaevskii (GP) equation with the current nonlinearity and external potentials. On the one hand, the introduction of two potentials (Pöschl-Teller and harmonic-Gaussian potentials) enables the discovery of exact soliton solutions in both focusing and defocusing cases. We analyze the interplay effects of current nonlinearity and potential on soliton stability via associated Bogoliubov-de Gennes equations. Moreover, multiple families of numerical solitons (ground-state and dipole modes) trapped in potentials are found, exhibiting distinctive structures. The interactions between solitons trapped in potentials are studied, which exhibit the inelastic trajectories and repulsive interactions. On the other hand, we introduce the time-dependent potentials such that the controlled RWs are found in both focusing and defocusing GP equations with current nonlinearity. Furthermore, through the interaction between potentials and current nonlinearity, it is possible to enlarge the region of modulational instability, leading to the generation of RWs and chiral solitons. High-order RWs are generated from several Gaussian perturbations on a continuous wave. The presence of current nonlinearity disrupts the structures of these high-order RWs, causing them to undergo a transform into chiral lower-amplitude solitons. Finally, various types of soliton excitations are investigated by varying the strengths of potential and current nonlinearity, showing the abundant dynamic transforms of chrital matter solitons.

On asymptotic stability of solitons for 2D Maxwell–Lorentz equations

We prove asymptotic stability of solitons for the 2D Maxwell–Lorentz equations with an extended charged particle. Soliton solutions correspond to the uniform motion of a particle. Our main result is as follows: the particle for large times moves asymptotically uniformly, and the Maxwell field asymptotically is the sum of the comoving field and the dispersive wave. The remainder converges to zero in the global energy norm.

Robust Three-Dimensional High-Order Solitons and Breathers in Driven Dissipative Systems: A Kerr Cavity Realization.

We present a general approach to excite robust dissipative three-dimensional and high-order solitons and breathers in passively driven nonlinear cavities. Our findings are illustrated in the paradigmatic example provided by an optical Kerr cavity with diffraction and anomalous dispersion, with the addition of an attractive three-dimensional parabolic potential. The potential breaks the translational symmetry along all directions, and impacts the system in a qualitatively unexpected manner: three-dimensional solitons, or light bullets, are the only existing and stable states for a given set of parameters. This property is extremely rare, if not unknown, in passive nonlinear systems. As a result, the excitation of the cavity with any input field leads to the deterministic formation of a target soliton or breather, with a spatiotemporal profile that unambiguously corresponds to the given cavity and pumping conditions. In addition, the tuning of the potential width along the temporal direction results in the existence of a plethora of stable asymmetric solitons. Our results may provide a solid route toward the observation of dissipative light bullets and three-dimensional breathers.

Vector gap solitons of spin-orbit-coupled Bose-Einstein condensate in honeycomb optical lattices.

The combination of the two hot topics of spin-orbit coupling and honeycomb lattices leads to the appearance of fascinating issues. In this paper, we investigate the existence and stability of vector gap solitons of spin-orbit-coupled Bose-Einstein condensates loaded in honeycomb optical lattices. The existence and stability of vector gap solitons are highly sensitive to the properties of interspin and intraspin atomic interaction. We numerically obtain the parametric dependence of the existence of vector gap solitons both in the semi-infinite gap and in the first gap. Since only dynamically stable localized modes in nonlinear systems are likely to be generated and observed in experiments, we examine the stability of the vector gap solitons by using the direct evolution dynamics, and obtain the phase diagram of stable and unstable vector gap solitons on the parameter plane of interspin and intraspin atomic interactions.

Soliton shedding of Pearcey-Gaussian beams with sidelobes

Taking the fractional Schrödinger equation as the theoretical model, the propagation characteristics of the Pearcey-Gaussian beams in the photorefractive medium are studied. The results show that stable breathing solitons can only be generated under certain conditions. The nonlinear coefficient and the Lévy index will change the maximum peak intensity and the breathing period of the soliton. The maximum peak intensity increases with the increase of the nonlinear coefficient but decreases with the increase of the Lévy index, whereas the breathing period of the soliton decreases with the increase of the nonlinear coefficient and the Lévy index. Besides, the interaction of double Pearcey-Gaussian beams in photorefractive media is also analyzed. By adjusting the beam amplitude, interval parameters and relative phase, the diffraction effect of the beams and the nonlinear effect of the medium are balanced to form a single breathing soliton or the double breathing solitons, so as to control the form and transmission process of the solitons. These properties can be used to manipulate beams, which have broad application prospects in optical trapping and particle trapping.

Soliton motion induced along ferromagnetic skyrmion chains in chiral thin nanotracks

Using atomistic magnetic simulations we investigate the soliton motion along a pinned skyrmion chain containing an interstitial skyrmion. We find that the soliton can exhibit stable motion along the chain without a skyrmion Hall effect for an extended range of drives. Under a constant drive the solitons have a constant velocity. We also measure the skyrmion velocity–current curves and identify the signatures of different phases including a pinned phase, stable soliton motion, and quasi-free motion at higher drives where all of the skyrmions depin from the pinning centers and move along the rigid wall. In the quasi-free motion regime, the velocity is oscillatory due to the motion of the skyrmions over the pinning sites. For increasing pinning strength, the onset of soliton motion shifts to higher values of current density. We also find that for stronger pinning, the characteristic velocity–current shape is affected by the annihilation of single or multiple skyrmions in the drive interval over which the soliton motion occurs. Our results indicate that stable skyrmion soliton motion is possible and that the solitons could be used as information carriers instead of the skyrmions themselves for technological applications.

ON THE GEOMETRY OF SPACELIKE MEAN CURVATURE FLOW SOLITONS IMMERSED IN A GRW SPACETIME

Abstract We investigate geometric aspects of complete spacelike mean curvature flow solitons of codimension one in a generalized Robertson–Walker (GRW) spacetime $-I\times _{f}M^n$ , with base $I\subset \mathbb R$ , Riemannian fiber $M^n$ and warping function $f\in C^\infty (I)$ . For this, we apply suitable maximum principles to guarantee that such a mean curvature flow soliton is a slice of the ambient space and to obtain nonexistence results concerning these solitons. In particular, we deal with entire graphs constructed over the Riemannian fiber $M^n$ , which are spacelike mean curvature flow solitons, and we also explore the geometry of a conformal vector field to establish topological and further rigidity results for compact (without boundary) mean curvature flow solitons in a GRW spacetime. Moreover, we study the stability of spacelike mean curvature flow solitons with respect to an appropriate stability operator. Standard examples of spacelike mean curvature flow solitons in GRW spacetimes are exhibited, and applications related to these examples are given.

Vortex solitons in large-scale waveguide arrays with adjustable discrete rotational symmetry

We consider vortex solitons in large-scale arrays composed of N elliptical waveguides placed on a ring, which can be fabricated using fs-laser writing technique in transparent nonlinear dielectrics. By introducing variable twist angles between longer axes of neighboring elliptical waveguides on a ring, we create circular arrays with adjustable discrete rotational symmetry ranging from CN to C1, when the number of waveguides N on the ring remains fixed. This allows to consider the impact of discrete rotational symmetry on the properties of available vortex solitons without changing the number of guiding channels in the structure, and to predict how exactly splitting of higher-order phase singularities into sets of charge-1 singularities occurs in vortex states, when they are forbidden by the discrete rotational symmetry of the structure that imposes the restrictions on the maximal possible vortex charge. It is found that separation between split charge-1 phase singularities in such higher-order vortex states increases with increase of the order of solution. We also study linear spectra of such arrays and show how variation of their discrete rotational symmetry affects linear eigenmodes, whose combinations can give rise to vortex modes. We also show that variation of discrete rotational symmetry in arrays with fixed number of guiding channels N has strong impact on stability of vortex solitons. Thus, only higher-charge vortex solitons are stable in such large-scale arrays and the number of stable states typically decreases with decrease of the order of discrete rotational symmetry of the structure at fixed N.

Asymptotic Stability of KdV Solitons on the Half-Line: A Study in the Energy Space

Asymptotic Stability of KdV Solitons on the Half-Line: A Study in the Energy Space

Conversion from Q-switched to bright-dark soliton pair mode-locked operation in an InSb based erbium-doped fiber laser

In this experiment, stable Q-switched pulses and bright-dark soliton pairs were realized in an InSb based erbium-doped fiber laser. Firstly, when the pump power was between 70 and 115 mW, a stable passive Q-switched operation with a central wavelength of 1565.38 nm was achieved, and the signal-to-noise ratio (SNR) was about 37 dB. As the pump power increased, the repetition frequency of the Q-switched pulse can be increased from 4.0145 to 10.623 kHz. When the pump power was increased to the range of 185 to 450 mW, stable bright-dark soliton pairs mode-locked operation was realized, and the two peaks of the spectrum were located at 1568.67 and 1569.34 nm, respectively. The pulse repetition rate was 3.419 MHz, and the SNR was about 59 dB. This research will broaden the application of InSb in ultrafast optics and nonlinear optics.