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
We investigate the alpha helical protein structure characterized by fourth-order interspine coupling,focusing on a three-coupled fourth-order nonlinear Schr??dinger system.We introduce a generalized Darboux transforma...We investigate the alpha helical protein structure characterized by fourth-order interspine coupling,focusing on a three-coupled fourth-order nonlinear Schr??dinger system.We introduce a generalized Darboux transformation,departing from the classical Darboux transformation.Based on this,we construct the two-and three-degenerate soliton solutions and four-degenerate asymptotic soliton solutions.Based on the asymptotic analysis,we find that the amplitudes of interacting solitons are retained upon the interactions.Elastic interactions between two degenerate solitons exhibiting four curve-type asymptotic solitons are depicted.When the lattice parameterβchanges,the velocities of the two degenerate solitons also change.Elastic interaction among three degenerate solitons comprising four curve-type asymptotic solitons and two line-type solitons is presented.Interaction among one soliton and two degenerate solitons with different velocities is shown.Elastic interaction among four degenerate solitons comprising eight curve-type asymptotic solitons is also presented.Interaction among two two-degenerate solitons with two spectral parameters is shown.The relative distance between two asymptotic solitons exhibits logarithmic growth with|t|,where t represents the retarded time.Acceleration of soliton separation decays exponentially with relative distance,and eventually approaches zero.Phase shifts depend on t.展开更多
We propose schemes for realizing various forms of bright solitons,bright vortices,and breathing solitons in a non-resonant,incoherently pumped exciton-polariton condensate system by introducing a two-dimensional Moir&...We propose schemes for realizing various forms of bright solitons,bright vortices,and breathing solitons in a non-resonant,incoherently pumped exciton-polariton condensate system by introducing a two-dimensional Moirélattice external potential.The symmetric shape of the soliton,at the center of the potential field is determined by the rotation angle of the twodimensional Moirélattice external potential.Within a specific range of rotation angles,the stability of the soliton is governed by the depth of the second sub-lattice.These two parameters mutually influence and constrain the soliton’s characteristics,and under certain rotation angles and sub-lattice depths,a bright vortex can be formed.At low pumping levels and with carefully chosen peak-to-valley positions in the external potential,the rotation angle becomes the primary factor controlling the distinct forms of breathing bright solitons.Our proposal provides effective schemes for the formation and control of various types of bright solitons and bright vortices in systems employing Moirélattice external potentials.This scheme for realizing polariton Bose-Einstein condensates(BECs)within a Moirélattice external potential also holds promise for advancing research in fields such as superfluidity and superconductivity.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
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 presents a generalized(2+1)-dimensional Sharma-Tasso-Olver-Burgers(STOB)equation,unifying dissipative and dispersive wave dynamics.By introducing an auxiliary potential𝑦as a new space variable and employing...We presents a generalized(2+1)-dimensional Sharma-Tasso-Olver-Burgers(STOB)equation,unifying dissipative and dispersive wave dynamics.By introducing an auxiliary potential𝑦as a new space variable and employing a simpler deformation algorithm,we deform the(1+1)-dimensional STOB model to higher dimensions.The resulting equation is proven Lax-integrable via introducing strong and weak Lax pairs.Traveling wave solutions of the(2+1)-dimensional STOB equation are derived through an ordinary differential equation reduction,with implicit solutions obtained for a special case.Crucially,we demonstrate that the system admits dispersionless decompositions into two types:Case 1 yields non-traveling twisted kink and bell solitons,while Case 2 involves complex implicit functions governed by cubic-algebraic constraints.Numerical visualizations reveal novel anisotropic soliton structures,and the decomposition methodology is shown to generalize broadly to other higher dimensional dispersionless decomposition solvable integrable systems.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
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
We explore the manipulation of gray-ring dark solitons in a two-component Bose gas with tunable soft-core interactions through numerical simulations of the time-dependent Gross-Pitaevskii equation.Our results demonstr...We explore the manipulation of gray-ring dark solitons in a two-component Bose gas with tunable soft-core interactions through numerical simulations of the time-dependent Gross-Pitaevskii equation.Our results demonstrate that the lifetime of gray solitons with periodically modulated soft-core interactions significantly depends on their initial depth.Specifically,shallower initial depths lead to longer lifetimes when exceeding a critical depth threshold.Furthermore,the soliton depth also governs the number and dynamic of vortex pairs resulting from the collapse of the ring dark soliton.These depth-dependent topological transformations open new perspectives for quantum manipulation.展开更多
This research paper seeks to investigate the characteristics of almost Riemann solitons and almost gradient Riemann solitons within the framework of generalized Robertson–Walker(GRW)spacetimes that incorporate imperf...This research paper seeks to investigate the characteristics of almost Riemann solitons and almost gradient Riemann solitons within the framework of generalized Robertson–Walker(GRW)spacetimes that incorporate imperfect fluids.Our study begins by defining specific properties of the potential vector field linked to these solitons.We examine the potential vector field of an almost Riemann soliton on GRW imperfect fluid spacetimes,establishing that it aligns collinearly with a unit timelike torse-forming vector field.This leads us to express the scalar curvature in relation to the structures of soliton and spacetime.Furthermore,we explore the characteristics of an almost gradient Riemann soliton with a potential functionψacross a range of GRW imperfect fluid spacetimes,deriving a formula for the Laplacian ofψ.We also categorize almost Riemann solitons on GRW imperfect fluid spacetimes into three types:shrinking,steady,and expanding,when the potential vector field of the soliton is Killing.We prove that a GRW imperfect fluid spacetime with constant scalar curvature and a Killing vector field admits an almost Riemann soliton.Additionally,we demonstrate that if the potential vector field of the almost Riemann soliton is aν(Ric)-vector,or if the GRW imperfect fluid spacetime is W_2-flat or pseudo-projectively flat,the resulting spacetime is classified as a dark fluid.展开更多
This study numerically estimates the momentum threshold required to excite solitons in anharmonic chains. For both Fermi–Pasta–Ulam–Tsingou(FPUT)-αβ and FPUT-β chains, regardless of whether the interatomic inter...This study numerically estimates the momentum threshold required to excite solitons in anharmonic chains. For both Fermi–Pasta–Ulam–Tsingou(FPUT)-αβ and FPUT-β chains, regardless of whether the interatomic interaction potential is symmetric, the required excitation momentum converges to the momentum of the soliton center(i.e., the peak momentum of the soliton) as the number of initially excited atoms increases. As the amplitude of the soliton approaches zero, the momentum threshold decreases to nearly zero, allowing soliton being excited with infinitesimal initial excitation momentum.These findings enhance the understanding of soliton dynamics and offer insights for optimizing soliton excitation methods,with potential applications in straintronics and nonlinear wave control technologies.展开更多
We study the existence and stability of dark-gap solitons in linear lattice and nonlinear lattices.The results indicate that the combination of linear and nonlinear lattices gives dark-gap solitons unique properties.T...We study the existence and stability of dark-gap solitons in linear lattice and nonlinear lattices.The results indicate that the combination of linear and nonlinear lattices gives dark-gap solitons unique properties.The linear lattice can stabilize dark-gap solitons,while the nonlinear lattice reduces the stability of dark-gap solitons.On the basis of numerical analysis,we investigate the effects of lattice depth,chemical potential,nonlinear lattice amplitude,and nonlinear lattice period on the soliton in mixed lattices with the same and different periods.The stability of dark-gap soliton is studied carefully by means of real-time evolution and linear stability analysis.Dark-gap solitons can exist stably in the band gap,but the solitons formed by the mixed lattices are slightly different when the period is the same or different.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 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
A direct renormalization method without spectrum theory is proposed to compute the perturbation of solitons in nearly integrable systems with multiple small parameters.The evolution equations of these parameters in un...A direct renormalization method without spectrum theory is proposed to compute the perturbation of solitons in nearly integrable systems with multiple small parameters.The evolution equations of these parameters in unperturbed solitons are obtained as the renormalization equations.Compared with routine methods,the advantages of the renormalization method are that the formulation is only based on a clear and simple mathematical theory,namely the Taylor expansion at a general point,the secular terms in perturbation series are eliminated automatically,any priori physical assumption on the form of the solution is avoided,multiple time scales arise naturally from the final naive perturbation expansion,and the Green’s function and corresponding spectrum of linear differential operators are not needed.As applications,the perturbation of solitons for KDV,MKdV and nonlinear Schrodinger equations,are obtained.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
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
By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （...By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （2＋1）-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.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 Natural Science Foundation of Shandong Province(Grant No.ZR2025QC30)。
文摘We investigate the alpha helical protein structure characterized by fourth-order interspine coupling,focusing on a three-coupled fourth-order nonlinear Schr??dinger system.We introduce a generalized Darboux transformation,departing from the classical Darboux transformation.Based on this,we construct the two-and three-degenerate soliton solutions and four-degenerate asymptotic soliton solutions.Based on the asymptotic analysis,we find that the amplitudes of interacting solitons are retained upon the interactions.Elastic interactions between two degenerate solitons exhibiting four curve-type asymptotic solitons are depicted.When the lattice parameterβchanges,the velocities of the two degenerate solitons also change.Elastic interaction among three degenerate solitons comprising four curve-type asymptotic solitons and two line-type solitons is presented.Interaction among one soliton and two degenerate solitons with different velocities is shown.Elastic interaction among four degenerate solitons comprising eight curve-type asymptotic solitons is also presented.Interaction among two two-degenerate solitons with two spectral parameters is shown.The relative distance between two asymptotic solitons exhibits logarithmic growth with|t|,where t represents the retarded time.Acceleration of soliton separation decays exponentially with relative distance,and eventually approaches zero.Phase shifts depend on t.
基金support from the Natural Science Foundation of Zhejiang Province of China (Grant No. LZ22A050002)the National Natural Science Foundation of China (Grant Nos. 12074343 and 11835011)support from the postdoctoral fellowship of Zhejiang Normal University (Grant No. YS304123952)
文摘We propose schemes for realizing various forms of bright solitons,bright vortices,and breathing solitons in a non-resonant,incoherently pumped exciton-polariton condensate system by introducing a two-dimensional Moirélattice external potential.The symmetric shape of the soliton,at the center of the potential field is determined by the rotation angle of the twodimensional Moirélattice external potential.Within a specific range of rotation angles,the stability of the soliton is governed by the depth of the second sub-lattice.These two parameters mutually influence and constrain the soliton’s characteristics,and under certain rotation angles and sub-lattice depths,a bright vortex can be formed.At low pumping levels and with carefully chosen peak-to-valley positions in the external potential,the rotation angle becomes the primary factor controlling the distinct forms of breathing bright solitons.Our proposal provides effective schemes for the formation and control of various types of bright solitons and bright vortices in systems employing Moirélattice external potentials.This scheme for realizing polariton Bose-Einstein condensates(BECs)within a Moirélattice external potential also holds promise for advancing research in fields such as superfluidity and superconductivity.
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 Foundations of China(Grant Nos.12235007,12375003,and 11975131).
文摘We presents a generalized(2+1)-dimensional Sharma-Tasso-Olver-Burgers(STOB)equation,unifying dissipative and dispersive wave dynamics.By introducing an auxiliary potential𝑦as a new space variable and employing a simpler deformation algorithm,we deform the(1+1)-dimensional STOB model to higher dimensions.The resulting equation is proven Lax-integrable via introducing strong and weak Lax pairs.Traveling wave solutions of the(2+1)-dimensional STOB equation are derived through an ordinary differential equation reduction,with implicit solutions obtained for a special case.Crucially,we demonstrate that the system admits dispersionless decompositions into two types:Case 1 yields non-traveling twisted kink and bell solitons,while Case 2 involves complex implicit functions governed by cubic-algebraic constraints.Numerical visualizations reveal novel anisotropic soliton structures,and the decomposition methodology is shown to generalize broadly to other higher dimensional dispersionless decomposition solvable integrable systems.
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.12175129,12475004,12175027,12005125)the Key Research Program of Frontier Sciences of the Chinese Academy of Sciences(Grant No.ZDBSLY7016)+4 种基金the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSY034)the Key Research and Development Projects of Shaanxi ProvinceChina(Grant No.2024GX-YBXM-564)the Scientific Research Program Funded by Shaanxi Provincial Education Department(Grant No.23JP020)the Youth Innovation Team of Shaanxi Universities。
文摘We explore the manipulation of gray-ring dark solitons in a two-component Bose gas with tunable soft-core interactions through numerical simulations of the time-dependent Gross-Pitaevskii equation.Our results demonstrate that the lifetime of gray solitons with periodically modulated soft-core interactions significantly depends on their initial depth.Specifically,shallower initial depths lead to longer lifetimes when exceeding a critical depth threshold.Furthermore,the soliton depth also governs the number and dynamic of vortex pairs resulting from the collapse of the ring dark soliton.These depth-dependent topological transformations open new perspectives for quantum manipulation.
文摘This research paper seeks to investigate the characteristics of almost Riemann solitons and almost gradient Riemann solitons within the framework of generalized Robertson–Walker(GRW)spacetimes that incorporate imperfect fluids.Our study begins by defining specific properties of the potential vector field linked to these solitons.We examine the potential vector field of an almost Riemann soliton on GRW imperfect fluid spacetimes,establishing that it aligns collinearly with a unit timelike torse-forming vector field.This leads us to express the scalar curvature in relation to the structures of soliton and spacetime.Furthermore,we explore the characteristics of an almost gradient Riemann soliton with a potential functionψacross a range of GRW imperfect fluid spacetimes,deriving a formula for the Laplacian ofψ.We also categorize almost Riemann solitons on GRW imperfect fluid spacetimes into three types:shrinking,steady,and expanding,when the potential vector field of the soliton is Killing.We prove that a GRW imperfect fluid spacetime with constant scalar curvature and a Killing vector field admits an almost Riemann soliton.Additionally,we demonstrate that if the potential vector field of the almost Riemann soliton is aν(Ric)-vector,or if the GRW imperfect fluid spacetime is W_2-flat or pseudo-projectively flat,the resulting spacetime is classified as a dark fluid.
文摘This study numerically estimates the momentum threshold required to excite solitons in anharmonic chains. For both Fermi–Pasta–Ulam–Tsingou(FPUT)-αβ and FPUT-β chains, regardless of whether the interatomic interaction potential is symmetric, the required excitation momentum converges to the momentum of the soliton center(i.e., the peak momentum of the soliton) as the number of initially excited atoms increases. As the amplitude of the soliton approaches zero, the momentum threshold decreases to nearly zero, allowing soliton being excited with infinitesimal initial excitation momentum.These findings enhance the understanding of soliton dynamics and offer insights for optimizing soliton excitation methods,with potential applications in straintronics and nonlinear wave control technologies.
基金supported by the Innovation Capability Improvement Project of Hebei Province,China(Grant No.22567605H).
文摘We study the existence and stability of dark-gap solitons in linear lattice and nonlinear lattices.The results indicate that the combination of linear and nonlinear lattices gives dark-gap solitons unique properties.The linear lattice can stabilize dark-gap solitons,while the nonlinear lattice reduces the stability of dark-gap solitons.On the basis of numerical analysis,we investigate the effects of lattice depth,chemical potential,nonlinear lattice amplitude,and nonlinear lattice period on the soliton in mixed lattices with the same and different periods.The stability of dark-gap soliton is studied carefully by means of real-time evolution and linear stability analysis.Dark-gap solitons can exist stably in the band gap,but the solitons formed by the mixed lattices are slightly different when the period is the same or different.
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 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supported by the Special Program for Ability Promotion of the Basic and Scientific Research(Grant No.2023JCYJ-01).
文摘A direct renormalization method without spectrum theory is proposed to compute the perturbation of solitons in nearly integrable systems with multiple small parameters.The evolution equations of these parameters in unperturbed solitons are obtained as the renormalization equations.Compared with routine methods,the advantages of the renormalization method are that the formulation is only based on a clear and simple mathematical theory,namely the Taylor expansion at a general point,the secular terms in perturbation series are eliminated automatically,any priori physical assumption on the form of the solution is avoided,multiple time scales arise naturally from the final naive perturbation expansion,and the Green’s function and corresponding spectrum of linear differential operators are not needed.As applications,the perturbation of solitons for KDV,MKdV and nonlinear Schrodinger equations,are obtained.
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.
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The project supported by the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05010 Acknowledgments The authors would like to thank professor Chun-Long Zheng for his fruitful and helpful suggestions.
文摘By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （2＋1）-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.
