Higher-order solitons in amplitude-disordered waveguide arrays

We investigate the existence and stability of different families of spatial solitons in optical waveguide arrays whose amplitudes obey a disordered distribution. The competition between focusing nonlinearity and linearly disordered refractive index modulation results in the formation of spatial localized nonlinear states. Solitons originating from Anderson modes with few nodes are robust during propagation. While multi-peaked solitons with in-phase neighboring components are completely unstable, multipole-mode solitons whose neighboring components are out-of-phase can propagate stably in wide parameter regions provided that their power exceeds a critical value. Our findings, thus, provide the first example of stable higher-order nonlinear states in disordered systems.

Higher-Order Nonlinear Effects on Optical Soliton Propagation and Their Interactions

When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order nonlinear Schr¨odinger equation, we analytically explore the evolution of optical solitons in the presence of highorder nonlinear effects. Moreover, the interactions between two nearby optical solitons and their transmission in a nonuniform fiber are investigated. The stability of optical soliton transmission and interactions are found to be destroyed to varying degrees due to higher-order nonlinear effects. The outcomes may offer some theoretical references for achieving ultra-high energy optical solitons in the future.

Photoinduced Floquet higher-order Weyl semimetal in C_(6) symmetric Dirac semimetals

Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges.Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

Pipeline thickness estimation using the dispersion of higher-order SH guided waves

Thickness measurement plays an important role in the monitoring of pipeline corrosion damage. However, the requirement for prior knowledge of the shear wave velocity in the pipeline material for popular ultrasonic thickness measurement limits its widespread application. This paper proposes a method that utilizes cylindrical shear horizontal(SH) guided waves to estimate pipeline thickness without prior knowledge of shear wave velocity. The inversion formulas are derived from the dispersion of higher-order modes with the high-frequency approximation. The waveform of the example problems is simulated using the real-axis integral method. The data points on the dispersion curves are processed in the frequency domain using the wave-number method. These extracted data are then substituted into the derived formulas. The results verify that employing higher-order SH guided waves for the evaluation of thickness and shear wave velocity yields less than1% error. This method can be applied to both metallic and non-metallic pipelines, thus opening new possibilities for health monitoring of pipeline structures.

Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).

Opinion consensus incorporating higher-order interactions in individual-collective networks

In the current information society, the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors are the research hot topics in the field of opinion dynamics. First, in this paper, a two-layer network consisting of an individual-opinion layer and a collective-opinion layer is constructed, and a dissemination model of opinions incorporating higher-order interactions(i.e. OIHOI dissemination model) is proposed. Furthermore, the dynamic equations of opinion dissemination for both individuals and groups are presented. Using Lyapunov's first method,two equilibrium points, including the negative consensus point and positive consensus point, and the dynamic equations obtained for opinion dissemination, are analyzed theoretically. In addition, for individual opinions and collective opinions,some conditions for reaching negative consensus and positive consensus as well as the theoretical expression for the dissemination threshold are put forward. Numerical simulations are carried to verify the feasibility and effectiveness of the proposed theoretical results, as well as the influence of the intra-structure, inter-connections, and higher-order interactions on the dissemination and evolution of individual opinions. The main results are as follows.(i) When the intra-structure of the collective-opinion layer meets certain characteristics, then a negative or positive consensus is easier to reach for individuals.(ii) Both negative consensus and positive consensus perform best in mixed type of inter-connections in the two-layer network.(iii) Higher-order interactions can quickly eliminate differences in individual opinions, thereby enabling individuals to reach consensus faster.

Time-Domain Higher-Order Boundary Element Method for Simulating High Forward-Speed Ship Motions in Waves

The hydrodynamic performance of a high forward-speed ship in obliquely propagating waves is numerically examined to assess both free motions and wave field in comparison with a low forward-speed ship.This numerical model is based on the time-domain potential flow theory and higher-order boundary element method,where an analytical expression is completely expanded to determine the base-unsteady coupling flow imposed on the moving condition of the ship.The ship in the numerical model may possess different advancing speeds,i.e.stationary,low speed,and high speed.The role of the water depth,wave height,wave period,and incident wave angle is analyzed by means of the accurate numerical model.It is found that the resonant motions of the high forward-speed ship are triggered by comparison with the stationary one.More specifically,a higher forward speed generates a V-shaped wave region with a larger elevation,which induces stronger resonant motions corresponding to larger wave periods.The shoaling effect is adverse to the motion of the low-speed ship,but is beneficial to the resonant motion of the high-speed ship.When waves obliquely propagate toward the ship,the V-shaped wave region would be broken due to the coupling effect between roll and pitch motions.It is also demonstrated that the maximum heave motion occurs in beam seas for stationary cases but occurs in head waves for high speeds.However,the variation of the pitch motion with period is hardly affected by wave incident angles.

A Study of a Moral Dilemma Stories Teaching Model Focusing on the Development of Higher-Order Thinking --"Synthetic polymers" as an example

Cultivating students'higher-order thinking is one of the important goals of modern education,and innovative teaching model is an effective way to achieve this goal.Aiming at the inadequacy of the existing moral dilemma stories approach in the transformation of knowledge and behavior,this research constructs a new Project Based Learning-Ethical Dilemma Stories(PBL-EDS)Teaching Model applicable to China's secondary education stage based on the innovative features of the moral dilemma stories approach on the core competencies,taking the chemistry subject as an example to carry out practice,and puts forward suggestions for the implementation of the teaching model.Chemistry as an example to carry out the practice,and suggestions are made for the implementation of the teaching model.

Higher-Order Dispersion and Soliton Pulse Compression in the Dispersion-Decreasing Fibers

The compression results of picosecond and femtosecond soliton pulses in the dispersion-decreasing fibers are reported in this paper.We found that the high-order dispersion has a great influence on the soliton compression.The expressions of optimum compression factor and optimum fiber length are obtained numerically.

Exact N-Soliton Solutions for the Higher-Order Nonlinear Schrödinger Equation Under Another Condition

By using a simple transformation approach,we solve the higher-order nonlinear Schrödinger equation under another condition.The obtained exact soliton solutions have the following prominent features:The bright soliton can propagate in both the normal and anormal regions;the soliton travelling speed is proportional to its amplitude square;the phase of the soliton is independent of its amplitude or width;and the component solitons of the bound soliton have the same phase.

Effective regulation of the interaction process among three optical solitons

The interaction between three optical solitons is a complex and valuable research direction,which is of practical application for promoting the development of optical communication and all-optical information processing technology.In this paper,we start from the study of the variable-coefficient coupled higher-order nonlinear Schodinger equation(VCHNLSE),and obtain an analytical three-soliton solution of this equation.Based on the obtained solution,the interaction of the three optical solitons is explored when they are incident from different initial velocities and phases.When the higher-order dispersion and nonlinear functions are sinusoidal,hyperbolic secant,and hyperbolic tangent functions,the transmission properties of three optical solitons before and after interactions are discussed.Besides,this paper achieves effective regulation of amplitude and velocity of optical solitons as well as of the local state of interaction process,and interaction-free transmission of the three optical solitons is obtained with a small spacing.The relevant conclusions of the paper are of great significance in promoting the development of high-speed and large-capacity optical communication,optical signal processing,and optical computing.

Nonautonomous solitons in the continuous wave background of the variable-coefficient higher-order nonlinear Schrodinger equation

We reduce the variable-coefficient higher-order nonlinear Schrodinger equation （VCHNLSE） into the constantcoefficient （CC） one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.

Darboux Transformation and New Soliton-like Solutions for （1＋1）-Dimensional Higher-Order Broer-Kaup System

In this letter, we construct a kind of new Darboux transformation for the （1＋1）-dimensional higher-order Broer-Kaup （HBK） system with the help of a gauge transformation of a spectral problem. By applying this new Darboux transformation, some new soliton-like solutions of the （1＋1）-dimensional HBK system are obtained.

Three-Wave Mixing of Dipole Solitons in One-Dimensional Quasi-Phase-Matched Nonlinear Crystals

A quasi-phase-matched technique is introduced for soliton transmission in a quadratic[χ^((2))]nonlinear crystal to realize the stable transmission of dipole solitons in a one-dimensional space under three-wave mixing.We report four types of solitons as dipole solitons with distances between their bimodal peaks that can be laid out in different stripes.We study three cases of these solitons:spaced three stripes apart,one stripe apart,and confined to the same stripe.For the case of three stripes apart,all four types have stable results,but for the case of one stripe apart,stable solutions can only be found atω_(1)=ω_(2),and for the condition of dipole solitons confined to one stripe,stable solutions exist only for Type1 and Type3 atω_(1)=ω_(2).The stability of the soliton solution is solved and verified using the imaginary time propagation method and real-time transfer propagation,and soliton solutions are shown to exist in the multistability case.In addition,the relations of the transportation characteristics of the dipole soliton and the modulation parameters are numerically investigated.Finally,possible approaches for the experimental realization of the solitons are outlined.

Nonlinear-Optical Analogies in Nuclear-Like Soliton Reactions:Selection Rules,Nonlinear Tunneling and Sub-Barrier Fusion–Fission

The main goal of our study is to reveal unexpected but intriguing analogies arising between optical solitons and nuclear physics,which still remain hidden from us.We consider the main cornerstones of the concept of nonlinear optics of nuclear reactions and the well-dressed repulsive-core solitons.On the base of this model,we reveal the most intriguing properties of the nonlinear tunneling of nucleus-like solitons and the soliton selfinduced sub-barrier transparency effect.We describe novel interesting and stimulating analogies between the interaction of nucleus-like solitons on the repulsive barrier and nuclear sub-barrier reactions.The main finding of this study concerns the conservation of total number of nucleons(or the baryon number)in nuclear-like soliton reactions.We show that inelastic interactions among well-dressed repulsive-core solitons arise only when a“cloud”of“dressing”spectral side-bands appears in the frequency spectra of the solitons.This property of nucleus-like solitons is directly related to the nuclear density distribution described by the dimensionless small shape-squareness parameter.Thus the Fourier spectra of nucleus-like solitons are similar to the nuclear form factors.We show that the nuclear-like reactions between well-dressed solitons are realized by“exchange”between“particle-like”side bands in their spectra.

Multiple Soliton Asymptotics in a Spin-1 Bose–Einstein Condensate

Spinor Bose–Einstein condensates(BECs)are formed when atoms in the multi-component BECs possess single hyperfine spin states but retain internal spin degrees of freedom.This study concentrates on a(1+1)-dimensional three-couple Gross–Pitaevskii system to depict the macroscopic spinor BEC waves within the meanfield approximation.Regarding the distribution of the atoms corresponding to the three vertical spin projections,a known binary Darboux transformation is utilized to derive the𝑁matter-wave soliton solutions and triple-pole matter-wave soliton solutions on the zero background,where𝑁is a positive integer.For those multiple matterwave solitons,the asymptotic analysis is performed to obtain the algebraic expressions of the soliton components in the𝑁matter-wave solitons and triple-pole matter-wave solitons.The asymptotic results indicate that the matter-wave solitons in the spinor BECs possess the property of maintaining their energy content and coherence during the propagation and interactions.Particularly,in the𝑁matter-wave solitons,each soliton component contributes to the phase shifts of the other soliton components;and in the triple-pole matter-wave solitons,stable attractive forces exist between the different matter-wave soliton components.Those multiple matter-wave solitons are graphically illustrated through three-dimensional plots,density plot and contour plot,which are consistent with the asymptotic analysis results.The present analysis may provide the explanations for the complex natural mechanisms of the matter waves in the spinor BECs,and may have potential applications in designs of atom lasers,atom interferometry and coherent atom transport.

Navigation Finsler metrics on a gradient Ricci soliton

In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.

Nondegenerate Soliton Solutions of(2+1)-Dimensional Multi-Component Maccari System

For a multi-component Maccari system with two spatial dimensions,nondegenerate one-soliton and two-soliton solutions are obtained with the bilinear method.It can be seen by drawing the spatial graphs of nondegenerate solitons that the real component of the system shows a cross-shaped structure,while the two solitons of the complex component show a multi-solitoff structure.At the same time,the asymptotic analysis of the interaction behavior of the two solitons is conducted,and it is found that under partially nondegenerate conditions,the real and complex components of the system experience elastic collision and inelastic collision,respectively.

Data-Driven Ai-and Bi-Soliton of the Cylindrical Korteweg-de Vries Equation via Prior-Information Physics-Informed Neural Networks

By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by simulating Ai-and Bi-soliton solutions of the cylindrical Korteweg-de Vries(cKdV)equation.

Three-Soliton Interactions and the Implementation of Their All-Optical Switching Function

As a key component in all-optical networks,all-optical switches play a role in constructing all-optical switching.Due to the absence of photoelectric conversion,all-optical networks can overcome the constraints of electronic bottlenecks,thereby improving communication speed and expanding their communication bandwidth.We study all-optical switches based on the interactions among three optical solitons.By analytically solving the coupled nonlinear Schr¨odinger equation,we obtain the three-soliton solution to the equation.We discuss the nonlinear dynamic characteristics of various optical solitons under different initial conditions.Meanwhile,we analyze the influence of relevant physical parameters on the realization of all-optical switching function during the process of three-soliton interactions.The relevant conclusions will be beneficial for expanding network bandwidth and reducing power consumption to meet the growing demand for bandwidth and traffic.