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 b...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.展开更多
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 non...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.展开更多
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...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.展开更多
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 no...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.展开更多
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 t...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.展开更多
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 processi...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.展开更多
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 ...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.展开更多
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 si...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.展开更多
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 ele...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.展开更多
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 ...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.展开更多
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 t...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.展开更多
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 main...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.展开更多
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 sol...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.展开更多
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 in...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.展开更多
In high-speed optical communication systems,in order to improve the communication rate,the distance between pulses must be compressed,which will cause the problem of the interaction between optical pulses in optical c...In high-speed optical communication systems,in order to improve the communication rate,the distance between pulses must be compressed,which will cause the problem of the interaction between optical pulses in optical communication systems,which has been widely concerned by researches.In this paper,the bilinear method will be used to analyze the coupled high-order nonlinear Schro¨dinger equations and obtain their three-soliton solutions.Then,the influence of the relevant parameters in the three-soliton solution on the soliton inelastic interaction is studied.In addition,the constraint conditions of each parameter in the three-soliton solution are analyzed,the inelastic interaction properties of optical solitons under different parameter conditions are obtained,and the relevant laws of the inelastic interaction of solitons are studied.The results will have potential applications in the soliton control,all-optical switching and optical computing.展开更多
We investigate the bounded travelling wave solutions of the Biswas-Arshed model(BAM)including the low group velocity dispersion and excluding the self-phase modulation.We integrate the nonlinear structure of the model...We investigate the bounded travelling wave solutions of the Biswas-Arshed model(BAM)including the low group velocity dispersion and excluding the self-phase modulation.We integrate the nonlinear structure of the model to obtain bounded optical solitons which pass through the optical fibers in the non-Kerr media.The bifurcation technique of the dynamical system is used to achieve the parameter bifurcation sets and split the parameter space into various areaswhich correspond to different phase portraits.All bounded optical solitons and bounded periodic wave solutions are identified and derived conforming to each region of these phase portraits.We also apply the extended sinh-Gordon equation expansion and the generalized Kudryashov integral schemes to obtain additional bounded optical soliton solutions of the BAM nonlinearity.We present more bounded optical shock waves,the bright-dark solitary wave,and optical rogue waves for the structure model via these schemes in different aspects.展开更多
For optical solitons with the pulse width in the subpicosecond and femtosecond scales in optical fibers,a modified model containing higher-order effects such as third-order dispersion and third-order nonlinearity is n...For optical solitons with the pulse width in the subpicosecond and femtosecond scales in optical fibers,a modified model containing higher-order effects such as third-order dispersion and third-order nonlinearity is needed.In this paper,in order to study the dynamic mechanism of femtosecond solitons in different media,we take the nonlinear Schr?dinger equation considering higher-order effects as the theoretical model,discuss the propagation of solitons in single-mode fibers,and explore the third-order dispersion and third-order nonlinear effects on the generation of optical solitons.The exact solution of the theoretical model is obtained through the bilinear method,and the transmission characteristics of two solitons with exact soliton solutions in actual fiber systems are analyzed and studied.The influence of various conditions on the transmission and interaction of optical solitons is explored.Methods for optimizing the transmission characteristics of optical solitons in optical communication systems are suggested.The relevant conclusions of this paper have guiding significance for improving the quality of fiber optic communication and increasing bit rates.展开更多
We present experimental observations of soliton pulsations in the net normal-dispersion fiber laser by using the dispersive Fourier transform(DFT) technique. According to the pulsating characteristics, the soliton pul...We present experimental observations of soliton pulsations in the net normal-dispersion fiber laser by using the dispersive Fourier transform(DFT) technique. According to the pulsating characteristics, the soliton pulsations are classified as visible and invisible soliton pulsations. The visible soliton pulsation is converted from single-into dual-soliton pulsation with the common characteristics of energy oscillation and bandwidth breathing. The invisible soliton pulsation undergoes periodic variation in the spectral profile and peak power but remains invariable in pulse energy. The reason for invisible soliton pulsation behavior is periodic oscillation of the pulse inside the soliton molecule. These results could be helpful in deepening our understanding of the soliton pulsation phenomena.展开更多
We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NL...We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities(especially the soliton accelerations and interaction forces);whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles,particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.展开更多
We take the higher-order nonlinear Schrodinger equation as a mathematical model and employ the bilinear method to analytically study the evolution characteristics of femtosecond solitons in optical fibers under higher...We take the higher-order nonlinear Schrodinger equation as a mathematical model and employ the bilinear method to analytically study the evolution characteristics of femtosecond solitons in optical fibers under higherorder nonlinear effects and higher-order dispersion effects.The results show that the effects have a significant impact on the amplitude and interaction characteristics of optical solitons.The larger the higher-order nonlinear coefficient,the more intense the interaction between optical solitons,and the more unstable the transmission.At the same time,we discuss the influence of other free parameters on third-order soliton interactions.Effectively regulate the interaction of three optical solitons by controlling relevant parameters.These studies will lay a theoretical foundation for experiments and further practicality of optical soliton communications.展开更多
基金Supported by the National Natural Science Foundation of China(11771020,12171005).
文摘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.
基金supported by the Scientific Research Foundation of Weifang University of Science and Technology (Grant Nos.KJRC2022002 and KJRC2023035)。
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.12274077 and 11874112)the Research Fund of the Guangdong Hong Kong Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology(Grant No.2020B1212030010)the Graduate Innovative Talents Training Program of Foshan University.
文摘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.
文摘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.
基金work was supported by the National Natural Science Foundation of China(Grant No.12161061)the Fundamental Research Funds for the Inner Mongolia University of Finance and Economics(Grant No.NCYWT23036)+2 种基金the Young innovative and Entrepreneurial Talents of the Inner Mongolia Grassland Talents Project in 2022,Autonomous Region“Five Ma-jor Tasks"Research Special Project for the Inner Mongo-lia University of Finance and Economics in 2024(Grant No.NCXWD2422)High Quality Research Achievement Cultivation Fund for the Inner Mongolia University of Fi-nance and Economics in 2024(Grant No.GZCG2426)the Talent Development Fund of Inner Mongolia.
文摘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.
基金supported by the Scientific Research Foundation of Weifang University of Science and Technology(Grant Nos.KJRC2022002 and KJRC2023035).
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.12375006)。
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.12175111 and 12235007)the K.C.Wong Magna Fund in Ningbo University。
文摘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.
基金supported by the Scientific Research Foundation of Weifang University of Science and Technology(Grant Nos.KJRC2022002 and KJRC2023035)。
文摘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.
基金supported by the Natural Science Foundation of Hebei Province,China (Grant No.A2021502004)the Fundamental Research Funds for the Central Universities (Grant No.2024MS126).
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12326305,11931017,and 12271490)the Excellent Youth Science Fund Project of Henan Province(Grant No.242300421158)+2 种基金the Natural Science Foundation of Henan Province(Grant No.232300420119)the Excellent Science and Technology Innovation Talent Support Program of ZUT(Grant No.K2023YXRC06)Funding for the Enhancement Program of Advantageous Discipline Strength of ZUT(2022)。
文摘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.
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘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.
文摘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.
基金the financial support from Science and Technology Project of the Jilin Provincial Department of Education (Grant No. JJKH20231171KJ)。
文摘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.
基金the National Natural Science Foundation of China(Grant Nos.11875009 and 11905016).
文摘In high-speed optical communication systems,in order to improve the communication rate,the distance between pulses must be compressed,which will cause the problem of the interaction between optical pulses in optical communication systems,which has been widely concerned by researches.In this paper,the bilinear method will be used to analyze the coupled high-order nonlinear Schro¨dinger equations and obtain their three-soliton solutions.Then,the influence of the relevant parameters in the three-soliton solution on the soliton inelastic interaction is studied.In addition,the constraint conditions of each parameter in the three-soliton solution are analyzed,the inelastic interaction properties of optical solitons under different parameter conditions are obtained,and the relevant laws of the inelastic interaction of solitons are studied.The results will have potential applications in the soliton control,all-optical switching and optical computing.
基金supported by the Deanship of ScientificResearch,Prince Sattam bin Abdulaziz University,Alkharj,Saudi Arabia,under Grant No.2021/01/19122.
文摘We investigate the bounded travelling wave solutions of the Biswas-Arshed model(BAM)including the low group velocity dispersion and excluding the self-phase modulation.We integrate the nonlinear structure of the model to obtain bounded optical solitons which pass through the optical fibers in the non-Kerr media.The bifurcation technique of the dynamical system is used to achieve the parameter bifurcation sets and split the parameter space into various areaswhich correspond to different phase portraits.All bounded optical solitons and bounded periodic wave solutions are identified and derived conforming to each region of these phase portraits.We also apply the extended sinh-Gordon equation expansion and the generalized Kudryashov integral schemes to obtain additional bounded optical soliton solutions of the BAM nonlinearity.We present more bounded optical shock waves,the bright-dark solitary wave,and optical rogue waves for the structure model via these schemes in different aspects.
基金Project supported by the Scientific Research Foundation of Weifang University of Science and Technology(Grant No.KJRC2022002)the Shandong Province Higher Educational Science and Technology Program(Grant No.J18KB108)the Research start-up fees for doctoral degree holders and senior professional title holders with master’s degrees of Binzhou University(Grant No.2022Y12)。
文摘For optical solitons with the pulse width in the subpicosecond and femtosecond scales in optical fibers,a modified model containing higher-order effects such as third-order dispersion and third-order nonlinearity is needed.In this paper,in order to study the dynamic mechanism of femtosecond solitons in different media,we take the nonlinear Schr?dinger equation considering higher-order effects as the theoretical model,discuss the propagation of solitons in single-mode fibers,and explore the third-order dispersion and third-order nonlinear effects on the generation of optical solitons.The exact solution of the theoretical model is obtained through the bilinear method,and the transmission characteristics of two solitons with exact soliton solutions in actual fiber systems are analyzed and studied.The influence of various conditions on the transmission and interaction of optical solitons is explored.Methods for optimizing the transmission characteristics of optical solitons in optical communication systems are suggested.The relevant conclusions of this paper have guiding significance for improving the quality of fiber optic communication and increasing bit rates.
基金supported by the National Natural Science Foundation of China (Grant No. 41875040)the Natural Science Foundation of Anhui Province, China (Grant No. 2008085MF211)+1 种基金the Foundation for Young Talents in College of Anhui Province, China (Grant No. gxyqZD2019034)the Innovation Fund for Postgraduates of Huaibei Normal University, China (Grant No. CX2022035)。
文摘We present experimental observations of soliton pulsations in the net normal-dispersion fiber laser by using the dispersive Fourier transform(DFT) technique. According to the pulsating characteristics, the soliton pulsations are classified as visible and invisible soliton pulsations. The visible soliton pulsation is converted from single-into dual-soliton pulsation with the common characteristics of energy oscillation and bandwidth breathing. The invisible soliton pulsation undergoes periodic variation in the spectral profile and peak power but remains invariable in pulse energy. The reason for invisible soliton pulsation behavior is periodic oscillation of the pulse inside the soliton molecule. These results could be helpful in deepening our understanding of the soliton pulsation phenomena.
基金Project supported by the Natural Science Foundation of Beijing Municipality (Grant No.1212007)the National Natural Science Foundation of China (Grant No.11705284)the Open Project Program of State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum (Grant No.PRP/DX-2211)。
文摘We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities(especially the soliton accelerations and interaction forces);whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles,particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.
基金Scientific Research Foundation of Weifang University of Science and Technology(Grant No.KJRC2022002)Shandong Province Higher Educational Science and Technology Program(Grant No.J18KB108)Research start-up fees for doctoral degree holders and senior professional title holders with master’s degrees of Binzhou University(Grant No.2022Y12)。
文摘We take the higher-order nonlinear Schrodinger equation as a mathematical model and employ the bilinear method to analytically study the evolution characteristics of femtosecond solitons in optical fibers under higherorder nonlinear effects and higher-order dispersion effects.The results show that the effects have a significant impact on the amplitude and interaction characteristics of optical solitons.The larger the higher-order nonlinear coefficient,the more intense the interaction between optical solitons,and the more unstable the transmission.At the same time,we discuss the influence of other free parameters on third-order soliton interactions.Effectively regulate the interaction of three optical solitons by controlling relevant parameters.These studies will lay a theoretical foundation for experiments and further practicality of optical soliton communications.
