This letter introduces the novel concept of Painlevé solitons—waves arising from the interaction between Painlevé waves and solitons in integrable systems.Painlevé solitons can also be viewed as solito...This letter introduces the novel concept of Painlevé solitons—waves arising from the interaction between Painlevé waves and solitons in integrable systems.Painlevé solitons can also be viewed as solitons propagating against a Painlevé wave background,in analogy to the established notion of elliptic solitons,which refers to solitons on an elliptic wave background.By employing a novel symmetry decomposition method aided by nonlocal residual symmetries,we explicitly construct (extended) Painlevé Ⅱ solitons for the Korteweg-de Vries equation and (extended) Painlevé Ⅳ solitons for the Boussinesq equation.展开更多
We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear...We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear Schr¨odinger equation.Beyond the fundamental nondegenerate one-soliton solution,we have identified and characterized nondegenerate breather bound state solitons,with particular emphasis on their evolution dynamics.展开更多
This study systematically investigates the attractor characteristics of harmonic solitons in a passively modelocked fiber laser.Through comprehensive analysis in both time and frequency domains,we examine the evolutio...This study systematically investigates the attractor characteristics of harmonic solitons in a passively modelocked fiber laser.Through comprehensive analysis in both time and frequency domains,we examine the evolution of pulse width,spectral bandwidth,and energy across different harmonic orders.The results demonstrate typical soliton attractor behaviors,including attractiveness,dissipativity,and self-organization.In the transition regions between harmonic orders,breathing harmonic soliton states are captured using the time-stretched dispersive Fourier transform.By comparing the breathing dynamics with the stable states,the existence and self-organizing nature of soliton attractors are further confirmed.Finally,harmonic soliton attractors are employed as programmable light sources to achieve ternary optical coding.展开更多
We investigate the dynamic behavior of vector soliton train propagating in optical media,modeled by the coherently coupled nonlinear Schrodinger(NLS)equation.It is shown that an increase in phase parameters,induces an...We investigate the dynamic behavior of vector soliton train propagating in optical media,modeled by the coherently coupled nonlinear Schrodinger(NLS)equation.It is shown that an increase in phase parameters,induces an increase in intensity of the periodic soliton train,as well as the number of pulses for each transverse electric(TE)and transverse magnetic(TM)mode.From the perturbation approach,when examining the propagation states for the transverse electric and magnetic(TEM)mode,we found a family of three bound-vector soliton states with a different propagation parameter at the first order,representing the three possible distinct vector optical fields reconfiguration of the initial profiles one of which is the‘replication’.At the second order,we obtain an eigenvalue problem with an optical external field,giving rise to five high intensity periodic vector soliton structures described by elliptic functions.Such vector soliton trains are intended to complement single-pulse solitons for multi-channel communication applications.展开更多
Recent theoretical verification of self-similar and dissipative pure-quartic solitons(PQSs)emphasized the similarity between PQS lasers and conventional fiber lasers,but the unique equilibrium mechanism hinders the fo...Recent theoretical verification of self-similar and dissipative pure-quartic solitons(PQSs)emphasized the similarity between PQS lasers and conventional fiber lasers,but the unique equilibrium mechanism hinders the formation of PQS molecules in normal fourth-order dispersion(FOD)regimes.In this paper,we investigated the effect of filters on shaping PQSs in normal FOD based on a passively mode-locked fiber laser model.A bandpass filter eliminates the time pedestal of dissipative PQSs,thus realizing a multi-pulsing state.When the filter bandwidth is appropriate,the effective spectral filtering effect can lower the pulse splitting threshold and enable the coherent restoration from chaotic PQSs to PQS molecules.Additionally,changing the central wavelength of the filter can generate PQSs and PQS molecules with asymmetric intensity distributions.These results are important guides for the manipulation of PQSs and the construction of high repetition-frequency fiber lasers.展开更多
Since the discovery of the electrostatic wave emissions such as broadband electrostatic noise(BEN)and electrostatic hiss in space plasmas,both kinetic and nonlinear fluid studies have been employed to study the proper...Since the discovery of the electrostatic wave emissions such as broadband electrostatic noise(BEN)and electrostatic hiss in space plasmas,both kinetic and nonlinear fluid studies have been employed to study the properties and characteristics of the solitons.Here,we use the Sagdeev pseudo-potential method to investigate the existence of the high-frequency supersolitons in a four-component unmagnetised plasma model composed of hot,warm,and cool electrons and cool ions species.All species are treated as adiabatic and are considered as stationary in our soliton analysis.Although the model supports both slow and fast electron-acoustic soliton,only the solutions of a negative-polarity supersoliton solution of the fast electron-acoustic type are discussed in this research study.It is shown that high-frequency supersoliton exists in a very narrower region of parameter space.Furthermore,the lower and upper Mach numbers for the supersolitons are computed and discussed.We have constructed the existence domains of the supersolitons,and the maximum potential amplitudes are computed.Positive potential supersolitons are not found in our numerical analysis.The importance and applications of our numerical findings in space-plasma environments are also discussed.展开更多
We propose a theoretical framework,based on the two-component Gross-Pitaevskii equation(GPE),for the investigation of vortex solitons(VSs)in hybrid atomic-molecular Bose-Einstein condensates under the action of the st...We propose a theoretical framework,based on the two-component Gross-Pitaevskii equation(GPE),for the investigation of vortex solitons(VSs)in hybrid atomic-molecular Bose-Einstein condensates under the action of the stimulated Raman-induced photoassociation and square-optical-lattice potential.Stationary solutions of the coupled GPE system are obtained by means of the imaginary-time integration,while the temporal dynamics are simulated using the fourth-order Runge-Kutta algorithm.The analysis reveals stable rhombus-shaped VS shapes with topological charges m=1 and 2 of the atomic component.The stability domains and spatial structure of these VSs are governed by three key parameters:the parametric-coupling strength(χ),atomicmolecular interaction strength(g_(12)),and the optical-lattice potential depth(V_(0)).By varyingχand g_(12),we demonstrate a structural transition where four-core rhombus-shaped VSs evolve into eight-core square-shaped modes,highlighting the nontrivial nonlinear dynamics of the system.This work establishes a connection between interactions of cold atoms and topologically structured matter waves in hybrid quantum systems.展开更多
The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
Optical solitons,as self-sustaining waveforms in a nonlinear medium where dispersion and nonlinear effects are balanced,have key applications in ultrafast laser systems and optical communications.Physics-informed neur...Optical solitons,as self-sustaining waveforms in a nonlinear medium where dispersion and nonlinear effects are balanced,have key applications in ultrafast laser systems and optical communications.Physics-informed neural networks(PINN)provide a new way to solve the nonlinear Schrodinger equation describing the soliton evolution by fusing data-driven and physical constraints.However,the grid point sampling strategy of traditional PINN suffers from high computational complexity and unstable gradient flow,which makes it difficult to capture the physical details efficiently.In this paper,we propose a residual-based adaptive multi-distribution(RAMD)sampling method to optimize the PINN training process by dynamically constructing a multi-modal loss distribution.With a 50%reduction in the number of grid points,RAMD significantly reduces the relative error of PINN and,in particular,optimizes the solution error of the(2+1)Ginzburg–Landau equation from 4.55%to 1.98%.RAMD breaks through the lack of physical constraints in the purely data-driven model by the innovative combination of multi-modal distribution modeling and autonomous sampling control for the design of all-optical communication devices.RAMD provides a high-precision numerical simulation tool for the design of all-optical communication devices,optimization of nonlinear laser devices,and other studies.展开更多
In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation ...In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV system.Then from a trivial seed solution,we construct soliton solutions.We also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.展开更多
In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci s...In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci solitons under certain condition about the Laplacian of thedistance function.展开更多
In the last few years,research on advanced ultrafast photonic devices has attracted great interest from laser physicists.As a semiconductor material with excellent nonlinear saturation absorption characteristics,Ga As...In the last few years,research on advanced ultrafast photonic devices has attracted great interest from laser physicists.As a semiconductor material with excellent nonlinear saturation absorption characteristics,Ga As has been used in solidstate and fiber lasers as a mode-locker.However,the pulse widths that have been reported in the searchable published literature are all long and the shortest is tens of picoseconds.Femtosecond pulse widths,desired for a variety of applications,have not yet been reported in Ga As-based pulsed lasers.In this work,we further explore the nonlinear characteristics of Ga As that has been magnetron sputtered onto the surface of a tapered fiber and its application in the generation of femtosecond lasing via effective dispersion optimization and nonlinearity management.With the enhanced interaction between evanescent waves and Ga As nanosheets,mode-locked soliton pulses as short as 830 fs are generated at repetition rates of 4.64 MHz.As far as we know,this is the first time that femtosecond-level pulses have been generated with a Ga As-based saturable absorber.In addition,soliton molecules,including in the dual-pulse state,are also realized under stronger pumping.This work demonstrates that Ga As-based photonic devices have good application prospects in effective polymorphous ultrashort pulsed laser generation.展开更多
The optical soliton characteristics of GaSb-based~2μm wavelength integrated optical chips have broad application prospects in optoelectronic fields such as optical communications,infrared countermeasures,and gas envi...The optical soliton characteristics of GaSb-based~2μm wavelength integrated optical chips have broad application prospects in optoelectronic fields such as optical communications,infrared countermeasures,and gas environment monitoring.In the research of two-section integrated optical chips,more attention is paid to their passive mode-locked characteristics.The ability of its structure to generate stable soliton transmission has not yet been studied,which will limit its further application in high-performance near-mid infrared optoelectronic technology.In this paper,we design and prepare a GaSb-based~2μm wave-length two-section integrated semiconductor laser chip structure,and test and analyze its related properties of soliton,includ-ing power−injection current−voltage(P−I−V),temperature and mode-locked characteristics.Experimental results show that the chip can achieve stable mode-locked operation at nearly~2μm wavelength and present the working characteristics of near opti-cal soliton states and multi-peak optical soliton states.By comparing and analyzing the measured optical pulse sequence curve with the numerical fitting based on the pure fourth order soliton approximation solution,it is confirmed that the two-section integrated optical chip structure can generate stable transmission of multi-peak optical soliton.This provides a research direc-tion for developing near-mid infrared mode-locked integrated optical chips with high-performance property of optical soliton.展开更多
We investigate dark solitons lying on elliptic function background in the defocusing Hirota equation with third-order dispersion and self-steepening terms.By means of the modified squared wavefunction method,we obtain...We investigate dark solitons lying on elliptic function background in the defocusing Hirota equation with third-order dispersion and self-steepening terms.By means of the modified squared wavefunction method,we obtain the Jacobi's elliptic solution of the defocusing Hirota equation,and solve the related linear matrix eigenvalue problem on elliptic function background.The elliptic N-dark soliton solution in terms of theta functions is constructed by the Darboux transformation and limit technique.The asymptotic dynamical behaviors for the elliptic N-dark soliton solution as t→±∞are studied.Through numerical plots of the elliptic one-,two-and three-dark solitons,the amplification effect on the velocity of elliptic dark solitons,and the compression effect on the soliton spatiotemporal distributions produced by the third-order dispersion and self-steepening terms are discussed.展开更多
This study presents a(2+1)-dimensional complex coupled dispersionless system.A Lax pair is proposed,and the Darboux transformation is employed to construct multisoliton solutions.These solutions exhibit a range of wav...This study presents a(2+1)-dimensional complex coupled dispersionless system.A Lax pair is proposed,and the Darboux transformation is employed to construct multisoliton solutions.These solutions exhibit a range of wave phenomena,including bright and dark solitons,S-shaped formations,parabolic profiles,and periodic wave patterns.Additionally,it is shown that the system is equivalent to the sine-Gordon equation and the negative flow of the modified Korteweg-de Vries hierarchy through appropriate transformations.展开更多
Magnetic solitons are nonlinear,local excitations in magnetic systems.In this study,we theoretically and numerically investigate the properties and generation of one-dimensional(1D)topologically trivial magnetic solit...Magnetic solitons are nonlinear,local excitations in magnetic systems.In this study,we theoretically and numerically investigate the properties and generation of one-dimensional(1D)topologically trivial magnetic solitons in ferromagnetic nanowires.An approximate analytical soliton solution described by two free parameters is validated by comparison with the micromagnetic simulation.Across an interface between two media of different anisotropy,the reflection and refraction of a soliton are highly nonlinear,which differ from linear spin waves.A pair of magnetic solitons that propagate in opposite directions can be generated by alternately applying magnetic-field or spin-polarized-current pulses of opposite directions to at least two successive regions.Each soliton corresponds to a soliton solution that can be controlled by the generation process.These magnetic solitons can be used to drive domain wall motion over a distance determined by the soliton magnitude,allowing for discrete manipulation of domain walls compatible with the digital nature of information technology.Our findings pave the way for the application of topologically trivial solitons in spintronics.展开更多
The existence and stability of the fundamental, multi-peak, and twisted solitons in Kerr nonlinear media with chirped(amplitude-modulated) lattices are reported. We discover that the chirp rate and lattice depth can d...The existence and stability of the fundamental, multi-peak, and twisted solitons in Kerr nonlinear media with chirped(amplitude-modulated) lattices are reported. We discover that the chirp rate and lattice depth can dramatically change the existence domain of solitons, the energy flow of solitons increases with increasing chirp rate or decreasing lattice depth.We also analyze how the chirp rate and lattice depth affect the stability of solitons. The stable domains of fundamental solitons and twisted solitons exhibit a multi-window distribution, while multi-peak solitons are unstable throughout the entire existence domain.展开更多
We study fundamental dark-bright solitons and the interaction of vector nonlinear Schr?dinger equations in both focusing and defocusing regimes.Classification of possible types of soliton solutions is given.There are ...We study fundamental dark-bright solitons and the interaction of vector nonlinear Schr?dinger equations in both focusing and defocusing regimes.Classification of possible types of soliton solutions is given.There are two types of solitons in the defocusing case and four types of solitons in the focusing case.The number of possible variations of two-soliton solutions depends on this classification.We demonstrate that only special types of two-soliton solutions in the focusing regime can generate breathers of the scalar nonlinear Schr?dinger equation.The cases of solitons with equal and unequal velocities in the superposition are considered.Numerical simulations confirm the validity of our exact solutions.展开更多
This article primarily establishes a two-soliton system and employs the Lewis-Riesenfeld invariant inverse control method to achieve shortcuts to adiabaticity(STA)technology.We study an atomic soliton Josephson juncti...This article primarily establishes a two-soliton system and employs the Lewis-Riesenfeld invariant inverse control method to achieve shortcuts to adiabaticity(STA)technology.We study an atomic soliton Josephson junctions(SJJs)device and subsequently compare and analyze it with atomic bosonic Josephson junctions.Moreover,we use higher-order expressions of the auxiliary equations to optimize the results and weaken the detrimental effect of the sloshing amplitude.We find that in the adiabatic shortcut evolution of two systems with time-containing tunnelling rates,the SJJs system is more robust over a rather short time evolution.In comparison with linear ramping,the STA technique is easier to achieve with the precise modulation of the quantum state in the SJJs system.展开更多
We theoretically and experimentally investigate thermal dynamics involved soliton microcomb generation in silicon oxynitride microresonators. Importantly, auxiliary laser heat balance scheme with flexible thermal mani...We theoretically and experimentally investigate thermal dynamics involved soliton microcomb generation in silicon oxynitride microresonators. Importantly, auxiliary laser heat balance scheme with flexible thermal manipulation is introduced to circumvent thermal instability and the intra-cavity temperature can be tuned from 60 ℃ to 41.5 ℃ via the commercial thermoelectric controller. As a result, various perfect soliton states with ultra-smooth spectral envelopes are observed on a well-designed and fabricated microresonator with homogeneous sidewall and thickness where spatial modes interaction and distortion are eliminated. The pre-reported spectral abrupt jumps due to mode hybridization are completely avoided and solitons tail oscillation vanishes simultaneously. This reported ideal coherent comb source without residual temporal and spectral noise will facilitate practical applications such as spectroscopy, ranging and astrocomb calibration.展开更多
基金supported by the National Natural Science Foundations of China (Grant Nos.12235007,12001424,12271324,and 12501333)the Natural Science Basic research program of Shaanxi Province (Grant Nos.2021JZ-21 and 2024JC-YBQN-0069)+3 种基金the China Postdoctoral Science Foundation (Grant Nos.2020M673332 and 2024M751921)the Fundamental Research Funds for the Central Universities (Grant No.GK202304028)the 2023 Shaanxi Province Postdoctoral Research Project (Grant No.2023BSHEDZZ186)Xi’an University,Xi’an Science and Technology Plan Wutongshu Technology Transfer Action Innovation Team(Grant No.25WTZD07)。
文摘This letter introduces the novel concept of Painlevé solitons—waves arising from the interaction between Painlevé waves and solitons in integrable systems.Painlevé solitons can also be viewed as solitons propagating against a Painlevé wave background,in analogy to the established notion of elliptic solitons,which refers to solitons on an elliptic wave background.By employing a novel symmetry decomposition method aided by nonlocal residual symmetries,we explicitly construct (extended) Painlevé Ⅱ solitons for the Korteweg-de Vries equation and (extended) Painlevé Ⅳ solitons for the Boussinesq equation.
基金supported by the National Natural Science Foundation of China(Grant Nos.12261131495 and 12475008)the Scientific Research and Developed Fund of Zhejiang A&F University(Grant No.2021FR0009)。
文摘We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear Schr¨odinger equation.Beyond the fundamental nondegenerate one-soliton solution,we have identified and characterized nondegenerate breather bound state solitons,with particular emphasis on their evolution dynamics.
基金supported by the National Natural Science Foundation of China(Grant No.12475008)the Scientific Research and Developed Fund of Zhejiang A&F University(Grant No.2021FR0009)。
文摘This study systematically investigates the attractor characteristics of harmonic solitons in a passively modelocked fiber laser.Through comprehensive analysis in both time and frequency domains,we examine the evolution of pulse width,spectral bandwidth,and energy across different harmonic orders.The results demonstrate typical soliton attractor behaviors,including attractiveness,dissipativity,and self-organization.In the transition regions between harmonic orders,breathing harmonic soliton states are captured using the time-stretched dispersive Fourier transform.By comparing the breathing dynamics with the stable states,the existence and self-organizing nature of soliton attractors are further confirmed.Finally,harmonic soliton attractors are employed as programmable light sources to achieve ternary optical coding.
文摘We investigate the dynamic behavior of vector soliton train propagating in optical media,modeled by the coherently coupled nonlinear Schrodinger(NLS)equation.It is shown that an increase in phase parameters,induces an increase in intensity of the periodic soliton train,as well as the number of pulses for each transverse electric(TE)and transverse magnetic(TM)mode.From the perturbation approach,when examining the propagation states for the transverse electric and magnetic(TEM)mode,we found a family of three bound-vector soliton states with a different propagation parameter at the first order,representing the three possible distinct vector optical fields reconfiguration of the initial profiles one of which is the‘replication’.At the second order,we obtain an eigenvalue problem with an optical external field,giving rise to five high intensity periodic vector soliton structures described by elliptic functions.Such vector soliton trains are intended to complement single-pulse solitons for multi-channel communication applications.
基金Project supported by the National Natural Science Foundation of China(Grant No.62175116)。
文摘Recent theoretical verification of self-similar and dissipative pure-quartic solitons(PQSs)emphasized the similarity between PQS lasers and conventional fiber lasers,but the unique equilibrium mechanism hinders the formation of PQS molecules in normal fourth-order dispersion(FOD)regimes.In this paper,we investigated the effect of filters on shaping PQSs in normal FOD based on a passively mode-locked fiber laser model.A bandpass filter eliminates the time pedestal of dissipative PQSs,thus realizing a multi-pulsing state.When the filter bandwidth is appropriate,the effective spectral filtering effect can lower the pulse splitting threshold and enable the coherent restoration from chaotic PQSs to PQS molecules.Additionally,changing the central wavelength of the filter can generate PQSs and PQS molecules with asymmetric intensity distributions.These results are important guides for the manipulation of PQSs and the construction of high repetition-frequency fiber lasers.
基金support of the University of Kwa Zulu Natalthe Walter Sisulu University。
文摘Since the discovery of the electrostatic wave emissions such as broadband electrostatic noise(BEN)and electrostatic hiss in space plasmas,both kinetic and nonlinear fluid studies have been employed to study the properties and characteristics of the solitons.Here,we use the Sagdeev pseudo-potential method to investigate the existence of the high-frequency supersolitons in a four-component unmagnetised plasma model composed of hot,warm,and cool electrons and cool ions species.All species are treated as adiabatic and are considered as stationary in our soliton analysis.Although the model supports both slow and fast electron-acoustic soliton,only the solutions of a negative-polarity supersoliton solution of the fast electron-acoustic type are discussed in this research study.It is shown that high-frequency supersoliton exists in a very narrower region of parameter space.Furthermore,the lower and upper Mach numbers for the supersolitons are computed and discussed.We have constructed the existence domains of the supersolitons,and the maximum potential amplitudes are computed.Positive potential supersolitons are not found in our numerical analysis.The importance and applications of our numerical findings in space-plasma environments are also discussed.
基金supported by the National Natural Science Foundation of China(Grant No.62275075)the Natural Science Foundation of Hubei Soliton Research Association(Grant No.2025HBSRA09)+1 种基金joint supported by Hubei Provincial Natural Science Foundation and Xianning of China(Grant Nos.2025AFD401 and 2025AFD405)Israel Science Foundation(Grant No.1695/22).
文摘We propose a theoretical framework,based on the two-component Gross-Pitaevskii equation(GPE),for the investigation of vortex solitons(VSs)in hybrid atomic-molecular Bose-Einstein condensates under the action of the stimulated Raman-induced photoassociation and square-optical-lattice potential.Stationary solutions of the coupled GPE system are obtained by means of the imaginary-time integration,while the temporal dynamics are simulated using the fourth-order Runge-Kutta algorithm.The analysis reveals stable rhombus-shaped VS shapes with topological charges m=1 and 2 of the atomic component.The stability domains and spatial structure of these VSs are governed by three key parameters:the parametric-coupling strength(χ),atomicmolecular interaction strength(g_(12)),and the optical-lattice potential depth(V_(0)).By varyingχand g_(12),we demonstrate a structural transition where four-core rhombus-shaped VSs evolve into eight-core square-shaped modes,highlighting the nontrivial nonlinear dynamics of the system.This work establishes a connection between interactions of cold atoms and topologically structured matter waves in hybrid quantum systems.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)National Natural Science Foundation of China(Grant No.12261131495)+1 种基金Beijing Municipal Science and Technology Commission,Adminitrative Commission of Zhongguancun Science Park(Grant No.Z231100006623006)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21)。
文摘Optical solitons,as self-sustaining waveforms in a nonlinear medium where dispersion and nonlinear effects are balanced,have key applications in ultrafast laser systems and optical communications.Physics-informed neural networks(PINN)provide a new way to solve the nonlinear Schrodinger equation describing the soliton evolution by fusing data-driven and physical constraints.However,the grid point sampling strategy of traditional PINN suffers from high computational complexity and unstable gradient flow,which makes it difficult to capture the physical details efficiently.In this paper,we propose a residual-based adaptive multi-distribution(RAMD)sampling method to optimize the PINN training process by dynamically constructing a multi-modal loss distribution.With a 50%reduction in the number of grid points,RAMD significantly reduces the relative error of PINN and,in particular,optimizes the solution error of the(2+1)Ginzburg–Landau equation from 4.55%to 1.98%.RAMD breaks through the lack of physical constraints in the purely data-driven model by the innovative combination of multi-modal distribution modeling and autonomous sampling control for the design of all-optical communication devices.RAMD provides a high-precision numerical simulation tool for the design of all-optical communication devices,optimization of nonlinear laser devices,and other studies.
基金Supported by the Jiangsu Higher School Undergraduate Innovation and Entrepreneurship Training Program(202311117078Y)。
文摘In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV system.Then from a trivial seed solution,we construct soliton solutions.We also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.
基金Supported by NSFC(Nos.12371051,12141101,11871126)。
文摘In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci solitons under certain condition about the Laplacian of thedistance function.
基金Project supported by the National Natural Science Foundation of China(Grant No.12164030)Young Science and Technology Talents of Inner Mongolia,China(Grant No.NJYT22101)+1 种基金the Central Government Guides Local Science,the Technology Development Fund Projects(Grant No.2023ZY0005)the Science and Technology Plan Projects of Inner Mongolia Autonomous Region of China(Grant No.2023KYPT0012)。
文摘In the last few years,research on advanced ultrafast photonic devices has attracted great interest from laser physicists.As a semiconductor material with excellent nonlinear saturation absorption characteristics,Ga As has been used in solidstate and fiber lasers as a mode-locker.However,the pulse widths that have been reported in the searchable published literature are all long and the shortest is tens of picoseconds.Femtosecond pulse widths,desired for a variety of applications,have not yet been reported in Ga As-based pulsed lasers.In this work,we further explore the nonlinear characteristics of Ga As that has been magnetron sputtered onto the surface of a tapered fiber and its application in the generation of femtosecond lasing via effective dispersion optimization and nonlinearity management.With the enhanced interaction between evanescent waves and Ga As nanosheets,mode-locked soliton pulses as short as 830 fs are generated at repetition rates of 4.64 MHz.As far as we know,this is the first time that femtosecond-level pulses have been generated with a Ga As-based saturable absorber.In addition,soliton molecules,including in the dual-pulse state,are also realized under stronger pumping.This work demonstrates that Ga As-based photonic devices have good application prospects in effective polymorphous ultrashort pulsed laser generation.
基金the National Natural Science Foundation of China(Grant Nos.62274048,62464006,62174046)the Ministry of Education,Singapore(Grant No.MOE-T2EP50121-0005)+1 种基金Hainan Province Science and Technology Special Fund(Grant No.ZDYF2025GXJS007)National Key R&D Program of China(Grant No.2023YFF0722400).
文摘The optical soliton characteristics of GaSb-based~2μm wavelength integrated optical chips have broad application prospects in optoelectronic fields such as optical communications,infrared countermeasures,and gas environment monitoring.In the research of two-section integrated optical chips,more attention is paid to their passive mode-locked characteristics.The ability of its structure to generate stable soliton transmission has not yet been studied,which will limit its further application in high-performance near-mid infrared optoelectronic technology.In this paper,we design and prepare a GaSb-based~2μm wave-length two-section integrated semiconductor laser chip structure,and test and analyze its related properties of soliton,includ-ing power−injection current−voltage(P−I−V),temperature and mode-locked characteristics.Experimental results show that the chip can achieve stable mode-locked operation at nearly~2μm wavelength and present the working characteristics of near opti-cal soliton states and multi-peak optical soliton states.By comparing and analyzing the measured optical pulse sequence curve with the numerical fitting based on the pure fourth order soliton approximation solution,it is confirmed that the two-section integrated optical chip structure can generate stable transmission of multi-peak optical soliton.This provides a research direc-tion for developing near-mid infrared mode-locked integrated optical chips with high-performance property of optical soliton.
基金supported by the National Natural Science Foundation of China(Grant No.12326304,12326305,12071304)the Shenzhen Natural Science Fund(the Stable Support Plan Program)(Grant No.20220809163103001)+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We investigate dark solitons lying on elliptic function background in the defocusing Hirota equation with third-order dispersion and self-steepening terms.By means of the modified squared wavefunction method,we obtain the Jacobi's elliptic solution of the defocusing Hirota equation,and solve the related linear matrix eigenvalue problem on elliptic function background.The elliptic N-dark soliton solution in terms of theta functions is constructed by the Darboux transformation and limit technique.The asymptotic dynamical behaviors for the elliptic N-dark soliton solution as t→±∞are studied.Through numerical plots of the elliptic one-,two-and three-dark solitons,the amplification effect on the velocity of elliptic dark solitons,and the compression effect on the soliton spatiotemporal distributions produced by the third-order dispersion and self-steepening terms are discussed.
文摘This study presents a(2+1)-dimensional complex coupled dispersionless system.A Lax pair is proposed,and the Darboux transformation is employed to construct multisoliton solutions.These solutions exhibit a range of wave phenomena,including bright and dark solitons,S-shaped formations,parabolic profiles,and periodic wave patterns.Additionally,it is shown that the system is equivalent to the sine-Gordon equation and the negative flow of the modified Korteweg-de Vries hierarchy through appropriate transformations.
基金supported by the National Natural Science Foundation of China(Grants Nos.11804045 and 12174093)the Natural Science Foundation of Hunan Province of China(Grant No.2025JJ60001)the Fundamental Research Funds for the Central Universities。
文摘Magnetic solitons are nonlinear,local excitations in magnetic systems.In this study,we theoretically and numerically investigate the properties and generation of one-dimensional(1D)topologically trivial magnetic solitons in ferromagnetic nanowires.An approximate analytical soliton solution described by two free parameters is validated by comparison with the micromagnetic simulation.Across an interface between two media of different anisotropy,the reflection and refraction of a soliton are highly nonlinear,which differ from linear spin waves.A pair of magnetic solitons that propagate in opposite directions can be generated by alternately applying magnetic-field or spin-polarized-current pulses of opposite directions to at least two successive regions.Each soliton corresponds to a soliton solution that can be controlled by the generation process.These magnetic solitons can be used to drive domain wall motion over a distance determined by the soliton magnitude,allowing for discrete manipulation of domain walls compatible with the digital nature of information technology.Our findings pave the way for the application of topologically trivial solitons in spintronics.
基金Project supported by the Science and Technology Project of Hebei Education Department, China (Grant No. ZD2020200)the Innovation Capability Improvement Project of Hebei Province, China (Grant No. 22567605H)。
文摘The existence and stability of the fundamental, multi-peak, and twisted solitons in Kerr nonlinear media with chirped(amplitude-modulated) lattices are reported. We discover that the chirp rate and lattice depth can dramatically change the existence domain of solitons, the energy flow of solitons increases with increasing chirp rate or decreasing lattice depth.We also analyze how the chirp rate and lattice depth affect the stability of solitons. The stable domains of fundamental solitons and twisted solitons exhibit a multi-window distribution, while multi-peak solitons are unstable throughout the entire existence domain.
基金supported by the NSFC(Grants Nos.12175178and 12247103)Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSY016)Graduate innovation project of Northwest University(Grant No.CX2024137)。
文摘We study fundamental dark-bright solitons and the interaction of vector nonlinear Schr?dinger equations in both focusing and defocusing regimes.Classification of possible types of soliton solutions is given.There are two types of solitons in the defocusing case and four types of solitons in the focusing case.The number of possible variations of two-soliton solutions depends on this classification.We demonstrate that only special types of two-soliton solutions in the focusing regime can generate breathers of the scalar nonlinear Schr?dinger equation.The cases of solitons with equal and unequal velocities in the superposition are considered.Numerical simulations confirm the validity of our exact solutions.
基金supported by the National Natural Science Foundation of China(Grant nos.12075145 and 12211540002)the Science and Technology Commission of Shanghai Municipal(Grant no.2019SHZDZX01-ZX04)。
文摘This article primarily establishes a two-soliton system and employs the Lewis-Riesenfeld invariant inverse control method to achieve shortcuts to adiabaticity(STA)technology.We study an atomic soliton Josephson junctions(SJJs)device and subsequently compare and analyze it with atomic bosonic Josephson junctions.Moreover,we use higher-order expressions of the auxiliary equations to optimize the results and weaken the detrimental effect of the sloshing amplitude.We find that in the adiabatic shortcut evolution of two systems with time-containing tunnelling rates,the SJJs system is more robust over a rather short time evolution.In comparison with linear ramping,the STA technique is easier to achieve with the precise modulation of the quantum state in the SJJs system.
基金supported by the National Natural Science Foundation of China(NSFC)(No.12204381,62205370)the fund of Natural Science Fundamental Research Program of Shaanxi Province(2023-JC-QN-0645)+1 种基金Startup Funding from Shanghai Institute of Optics and Fine Mechanics,Chinese Academy of Science(24JR521001)Shanghai Magnolia Talent Plan Pujiang Project(24PJD125).
文摘We theoretically and experimentally investigate thermal dynamics involved soliton microcomb generation in silicon oxynitride microresonators. Importantly, auxiliary laser heat balance scheme with flexible thermal manipulation is introduced to circumvent thermal instability and the intra-cavity temperature can be tuned from 60 ℃ to 41.5 ℃ via the commercial thermoelectric controller. As a result, various perfect soliton states with ultra-smooth spectral envelopes are observed on a well-designed and fabricated microresonator with homogeneous sidewall and thickness where spatial modes interaction and distortion are eliminated. The pre-reported spectral abrupt jumps due to mode hybridization are completely avoided and solitons tail oscillation vanishes simultaneously. This reported ideal coherent comb source without residual temporal and spectral noise will facilitate practical applications such as spectroscopy, ranging and astrocomb calibration.
