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Higher-Order Nonlinear Effects on Optical Soliton Propagation and Their Interactions
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作者 伊厚会 李晓凤 +2 位作者 张俊玲 张鑫 马国利 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第7期53-57,共5页
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
关键词 NONLINEAR solitonS soliton
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Data-Driven Ai-and Bi-Soliton of the Cylindrical Korteweg-de Vries Equation via Prior-Information Physics-Informed Neural Networks
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作者 田十方 李彪 张钊 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第3期1-6,共6页
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
关键词 equation soliton CYLINDRICAL
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Three-Soliton Interactions and the Implementation of Their All-Optical Switching Function
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作者 伊厚会 张鑫 +3 位作者 石领先 姚延立 王树斌 马国利 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第4期51-58,共8页
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
关键词 soliton EXPANDING NETWORKS
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An integrable generalization of the Fokas–Lenells equation:Darboux transformation, reduction and explicit soliton solutions
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作者 魏姣 耿献国 王鑫 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第7期117-124,共8页
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
关键词 Darboux transformation soliton solutions generalized Fokas–Lenells equation
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Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schr¨odinger equation with sextic operator under non-zero boundary conditions
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作者 Luyao Zhang Xiyang Xie 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第9期268-280,共13页
We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinearSchr¨odinger equation with the sextic operator under non-zero boundary conditions. Our analysis... We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinearSchr¨odinger 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
关键词 double-pole solitonS double-pole BREAtheRS Riemann–Hilbert problem non-zero boundary conditions nonlinear Schr¨odinger equation with sextic OPERATOR
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Matrix integrable fifth-order mKdV equations and their soliton solutions 被引量:2
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作者 马文秀 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第2期47-52,共6页
We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems,... We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifthorder mKdV equations are given. 展开更多
关键词 matrix integrable equation Riemann–Hilbert problem soliton
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THE SASA-SATSUMA EQUATION ON A NON-ZERO BACKGROUND: THE INVERSE SCATTERING TRANSFORM AND MULTI-SOLITON SOLUTIONS 被引量:1
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作者 温丽丽 范恩贵 陈勇 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1045-1080,共36页
We concentrate on the inverse scattering transformation for the Sasa-Satsuma equation with 3×3 matrix spectrum problem and a nonzero boundary condition. To circumvent the multi-value of eigenvalues, we introduce ... We concentrate on the inverse scattering transformation for the Sasa-Satsuma equation with 3×3 matrix spectrum problem and a nonzero boundary condition. To circumvent the multi-value of eigenvalues, we introduce a suitable two-sheet Riemann surface to map the original spectral parameter k into a single-valued parameter z. The analyticity of the Jost eigenfunctions and scattering coefficients of the Lax pair for the Sasa-Satsuma equation are analyzed in detail. According to the analyticity of the eigenfunctions and the scattering coefficients, the z-complex plane is divided into four analytic regions of D_(j) : j = 1, 2, 3, 4. Since the second column of Jost eigenfunctions is analytic in D_(j), but in the upper-half or lowerhalf plane, we introduce certain auxiliary eigenfunctions which are necessary for deriving the analytic eigenfunctions in Dj. We find that the eigenfunctions, the scattering coefficients and the auxiliary eigenfunctions all possess three kinds of symmetries;these characterize the distribution of the discrete spectrum. The asymptotic behaviors of eigenfunctions, auxiliary eigenfunctions and scattering coefficients are also systematically derived. Then a matrix Riemann-Hilbert problem with four kinds of jump conditions associated with the problem of nonzero asymptotic boundary conditions is established, from this N-soliton solutions are obtained via the corresponding reconstruction formulae. The reflectionless soliton solutions are explicitly given. As an application of the N-soliton formula, we present three kinds of single-soliton solutions according to the distribution of discrete spectrum. 展开更多
关键词 Sasa-Satsuma equation nonzero boundary condition auxiliary eigenfunctions Riemann-Hilbert problem soliton solution
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Effective Control of Three Soliton Interactions for the High-Order Nonlinear Schrodinger Equation
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作者 姚延立 伊厚会 +1 位作者 张鑫 马国利 《Chinese Physics Letters》 SCIE EI CAS CSCD 2023年第10期24-28,共5页
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
关键词 solitonS soliton NONLINEAR
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High-order effect on the transmission of two optical solitons
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作者 伊厚会 姚延立 +1 位作者 张鑫 马国利 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第10期363-366,共4页
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
关键词 nonlinear optics optical communication system optical solitons solitons interaction
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Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schr?dinger equation
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作者 张雪峰 许韬 +1 位作者 李敏 孟悦 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第1期244-252,共9页
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
关键词 nonlinear Schr?dinger equation soliton solutions asymptotic analysis soliton interactions
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Influence of the initial parameters on soliton interaction in nonlinear optical systems
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作者 张昕仪 吴晔 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第7期325-328,共4页
In nonlinear optical systems,optical solitons have the transmission properties of reducing error rate,improving system security and stability,and have important research significance in future research on all optical ... In nonlinear optical systems,optical solitons have the transmission properties of reducing error rate,improving system security and stability,and have important research significance in future research on all optical communication.This paper uses the bilinear method to obtain the two-soliton solutions of the nonlinear Schrödinger equation.By analyzing the relevant physical parameters in the obtained solutions,the interaction between optical solitons is optimized.The influence of the initial conditions on the interactions of the optical solitons is analyzed in detail,the reason why the interaction of the optical solitons is sensitive to the initial condition is discussed,and the interactions of the optical solitons are effectively weakened.The relevant results are beneficial for reducing the error rate and promoting the communication quality of the system. 展开更多
关键词 optical solitons nonlinear Schrödinger equation soliton interactions
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Bifurcation Analysis and Bounded Optical Soliton Solutions of the Biswas-Arshed Model
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作者 Fahad Sameer Alshammari Md Fazlul Hoque +1 位作者 Harun-Or-Roshid Muhammad Nadeem 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第6期2197-2217,共21页
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
关键词 the Biswas-Arshed model the extended sinh-Gordon equation expansion the generalized Kudryashov approach shock wave double solitons optical singular double solitons chirp-free bright-dark double solitons
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Solitons and Bifurcations for the Generalized Tzitzéica Type Equation in Nonlinear Fiber Optics
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作者 Xujie Jiang 《Journal of Applied Mathematics and Physics》 2023年第10期3042-3060,共19页
Solitons and bifurcations for the generalized Tzitzéica type equation are studied by using the theory of dynamical systems and Hamilton function. With the help of Maple and bifurcation theory of differential equa... Solitons and bifurcations for the generalized Tzitzéica type equation are studied by using the theory of dynamical systems and Hamilton function. With the help of Maple and bifurcation theory of differential equations, the bifurcation parameter conditions and all the bifurcation phase portraits are obtained. Because the same energy value of the Hamiltonian function is corresponding to the same orbit, thus the periodic wave solutions, bright soliton and dark soliton solutions are defined. 展开更多
关键词 Generalized Tzitzéica Type Equation Homoclinic Orbit Periodic Wave Solution Bright soliton Dark soliton
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Riemann-Hilbert approach of the complex Sharma-Tasso-Olver equation and its N-soliton solutions
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作者 李莎 夏铁成 魏含玉 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第4期130-134,共5页
We study the complex Sharma-Tasso-Olver equation using the Riemann-Hilbert approach.The associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem ... We study the complex Sharma-Tasso-Olver equation using the Riemann-Hilbert approach.The associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem of the Lax pair.Subsequently,in the case that the Riemann-Hilbert problem is irregular,the N-soliton solutions of the equation can be deduced.In addition,the three-dimensional graphic of the soliton solutions and wave propagation image are graphically depicted and further discussed. 展开更多
关键词 complex Sharma-Tasso-Olver equation Riemann-Hilbert problem spectral problem soliton solutions
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Nondegenerate solitons of the(2+1)-dimensional coupled nonlinear Schrodinger equations with variable coefficients in nonlinear optical fibers
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作者 杨薇 程雪苹 +1 位作者 金桂鸣 王佳楠 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期170-178,共9页
We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota b... We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one. 展开更多
关键词 nondegenerate solitons variable coefficients coupled nonlinear Schr?dinger equations Hirota bilinear method
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Adjusting amplitude of the stored optical solitons by inter-dot tunneling coupling in triple quantum dot molecules
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作者 王胤 周驷杰 +1 位作者 邓永和 陈桥 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第5期433-441,共9页
We study the propagation properties of a probe field in an aligned asymmetric triple quantum dot molecule with both sides inter-dot tunneling coupling effect. It is shown that the probe field can form optical soliton ... We study the propagation properties of a probe field in an aligned asymmetric triple quantum dot molecule with both sides inter-dot tunneling coupling effect. It is shown that the probe field can form optical soliton due to the destructive quantum interference induced by the quantum inter-dot tunneling coupling effect. Interestingly, these optical solitons can be stored and retrieved by adjusting single or double inter-dot tunneling coupling effect, different from that light memory in the ultra-cold atom system. Furthermore, we also find that the amplitude of the stored optical soliton can be adjusted by the strength of the single or double inter-dot tunneling coupling. It is possible to improve the stability and the fidelity of the optical information in the process of the storage and retrieval in semiconductor quantum dots devices. 展开更多
关键词 tunneling induced transparency triple quantum dot molecules the storage and retrieval of the optical solitons
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Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4×4 Lax pair
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作者 刘雪珂 闻小永 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期179-191,共13页
Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the co... Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics. 展开更多
关键词 discrete coupled mKdV equation continuous limit discrete generalized(r N-r)-fold Darboux transformation multi-soliton solutions rational soliton solutions
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Soliton molecules,T-breather molecules and some interaction solutions in the(2+1)-dimensional generalized KDKK equation
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作者 张艺源 刘子琪 +1 位作者 齐家馨 安红利 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第3期164-173,共10页
By employing the complexification method and velocity resonant principle to N-solitons of the(2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt(KDKK)equation,we obtain the soliton molecules,T-br... By employing the complexification method and velocity resonant principle to N-solitons of the(2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt(KDKK)equation,we obtain the soliton molecules,T-breather molecules,T-breather–L-soliton molecules and some interaction solutions when N≤6.Dynamical behaviors of these solutions are discussed analytically and graphically.The method adopted can be effectively used to construct soliton molecules and T-breather molecules of other nonlinear evolution equations.The results obtained may be helpful for experts to study the related phenomenon in oceanography and atmospheric science. 展开更多
关键词 soliton molecules breather molecules interaction solutions velocity resonant principle Konopelchenko–Dubrovsky–Kaup–Kupershmidt(KDKK)equation
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Three-Wave Mixing of Dipole Solitons in One-Dimensional Quasi-Phase-Matched Nonlinear Crystals
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作者 郭宇欣 徐晓喜 +5 位作者 陈招拼 周延桂 刘彬 和河向 黎永耀 谢嘉宁 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第1期25-33,共9页
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
关键词 soliton solitonS DIPOLE
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Multiple Soliton Asymptotics in a Spin-1 Bose–Einstein Condensate
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作者 Zhong-Zhou Lan 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第9期15-22,共8页
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
关键词 soliton solitonS ASYMPTOTIC
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