Possible ion-acoustic soliton formation in the ionospheric perturbations observed on DEMETER before the 2007 Pu'er earthquake

The data of ionospheric perturbations observed on DEMETER before the 2007 Pu＇er earthquake are analyzed. The three-component plasma （ions, electrons and heavy ions） is studied in the fluid concept. The linear dispersion relation for ion-acoustic wave is found in the presence of heavy ions. The nonlinear dynamics is studied for arbitrary amplitude of the wave. The Sagdeev potential is calculated, which shows that solitary structure exists for Mach number within a range defined by the presence of heavy ions. The developed ion-acoustic solitons may be used as precursor for earthquake prediction.

The Kadomtsev-Petviashvili equation for dust ion-acoustic solitons in pair-ion plasmas

Using the reductive perturbation method,we have derived the Kadomtsev-Petviashvili（KP） equation to study the nonlinear properties of electrostatic collisionless dust ion-acoustic solitons in pair-ion（p-i） plasmas.We have chosen the fluid model for the positive ions,the negative ions,and a fraction of static charged（both positively and negatively） dust particles.Numerical solutions of these dust ion-acoustic solitons are plotted and their characteristics are discussed.It is found that only the amplitudes of the electrostatic dust ion-acoustic solitons vary when the dust is introduced in the pair-ion plasma.It is also noticed that the amplitude and the width of these solitons both vary when the thermal energy of the positive or negative ions is varied.It is shown that potential hump structures are formed when the temperature of the negative ions is higher than that of the positive ions,and potential dip structures are observed when the temperature of the positive ions supersedes that of the negative ions.As the pair-ion plasma mimics the electron-positron plasma,thus our results might be helpful in understanding the nonlinear dust ion acoustic solitary waves in super dense astronomical bodies.

Coupling Alfvénic and Ion-Acoustic Solitons

An exact nonlinear equation governing the coupling Alfvénic and ion-acoustic solitons and criterion for their existence are presented.For the case of low-β plasmas,the two modes decouple.In the small amplitude limit,the analytical results lead to KdV solitons.

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.

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.

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.

Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.

An integrable generalization of the Fokas–Lenells equation:Darboux transformation, reduction and explicit soliton solutions

Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.

Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrodinger equation with sextic operator under non-zero boundary conditions

We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.

High-Order Solitons and Hybrid Behavior of (3 + 1)-Dimensional Potential Yu-Toda-Sasa-Fukuyama Equation with Variable Coefficients

In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton solution. By using the long wave limit method, the N-order rational solution can be obtained from N-order soliton solution. Then, through the paired complexification of parameters, the lump solution is obtained from N-order rational solution. Meanwhile, we obtained a hybrid solution between 1-lump solution and N-soliton (N=1,2) by using the long wave limit method and parameter complex. Furthermore, four different sets of three-dimensional graphs of solitons, lump solutions and hybrid solutions are drawn by selecting four different sets of coefficient functions which include one set of constant coefficient function and three sets of variable coefficient functions.

Non-Linear Ion-Acoustic Solitary Waves in Electron-Positron-Ion Plasma with Non-Thermal Electrons

Ion-acoustic solitary (IAS) waves in electron-positron-ion (e-p-i) plasma have been of interest to many researchers probably due to their relevance in understanding the Universe. However, the study of non-linear ion-acoustic waves in e-p-i plasma with non-thermal electrons has not been adequately studied. A theoretical investigation on non-linear IAS waves in e-p-i plasma comprising of warm inertial adiabatic fluid ions and electrons that are kappa distributed, and Boltzman distributed positron is presented here using the Sagdeev potential technique. It was found that existence domains of finite amplitude IAS waves were confined within the limits of minimum and maximum Mach numbers with varying k values. For lower values of k, the amplitude of the solitary electrostatic potential structures increased as the width decreased, while for high values, the potential amplitude decreased as the width of the solitary structure increased.

Ion-Acoustic Shock Waves in Nonextensive Electron-Positron-Ion Plasma

A rigorous theoretical investigation is made of ion-acoustic shock structures in an unmagnetized three-component plasma whose constituents are nonextensive electrons, nonextensive positrons, and inertial ions. The Burgers equation is derived by employing the reductive perturbation method. The effects of electron and positron nonextensivity and ion kinematic viscosity on the properties of these ion-acoustic shock waves are briefly discussed. It is found that shock waves with positive and negative potentials are obtained to depend on the plasma parameters. The entailment of our results may be useful to understand some astrophysical and cosmological scenarios including stellar polytropes, hadronic matter and quark-gluon plasma, protoneutron stars, dark-matter halos, etc., where effects of nonextensivity can play significant roles.

Weakly Nonlinear Quantum Dust Ion-Acoustic Waves

The one-dimensional quantum hydrodynamic (QHD) model for a three-specie quantum plasma is used to study the quantum counterpart of the well known dust ion-acoustic wave (DIAW). It is found that owing to the quantum effects, the dynamics of small but finite amplitude quantum dust ion-acoustic waves (QDIA) is governed by a deformed Korteweg-de Vries equation (dK-dV). The latter admits compressive as well as rarefactive stationary QDIA solitary wave solution. In the fully quantum case, the QDIA soliton experiences a spreading which becomes more significant as electron depletion is enhanced.

Comprehensive analysis of pure-quartic soliton dynamics in a passively mode-locked fiber laser

The understanding of soliton dynamics promotes the development of ultrafast laser technology. High-energy purequartic solitons(PQSs) have gradually become a hotspot in recent years. Herein, we numerically study the influence of the gain bandwidth, saturation power, small-signal gain, and output coupler on PQS dynamics in passively mode-locked fiber lasers. The results show that the above four parameters can affect PQS dynamics. Pulsating PQSs occur as we alter the other three parameters when the gain bandwidth is 50 nm. Meanwhile, PQSs evolve from pulsating to erupting and then to splitting as the other three parameters are altered when the gain bandwidth is 10 nm, which can be attributed to the existence of the spectral filtering effect and intra-cavity fourth-order dispersion. These findings provide new insights into PQS dynamics in passively mode-locked fiber lasers.