We study a generalized higher-order nonlinear Schr¨odinger equation in an optical fiber or a planar waveguide.We obtain the Lax pair and N-fold Darboux transformation(DT)with N being a positive integer.Based on L...We study a generalized higher-order nonlinear Schr¨odinger equation in an optical fiber or a planar waveguide.We obtain the Lax pair and N-fold Darboux transformation(DT)with N being a positive integer.Based on Lax pair obtained by us,we derive the infinitely-many conservation laws.We give the bright one-,two-,and N-soliton solutions,and the first-,second-,and Nth-order breather solutions based on the N-fold DT.We conclude that the velocities of the bright solitons are influenced by the distributed gain function,g(z),and variable coefficients in equation,h_(1)(z),p_(1)(z),r_(1)(z),and s_(1)(z)via the asymptotic analysis,where z represents the propagation variable or spatial coordinate.We also graphically observe that:the velocities of the first-and second-order breathers will be affected by h_(1)(z),p_(1)(z),r_(1)(z),and s_(1)(z),and the background wave depends on g(z).展开更多
We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis main...We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.展开更多
We study a two-dimensional （2D） diatomic lattice of anhaxmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers （DBs） can be explicitly constructed by an exact separation of...We study a two-dimensional （2D） diatomic lattice of anhaxmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers （DBs） can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers （QDBs） and chaotic discrete breathers （CDBs） by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.展开更多
Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam （FPU） lattice with linear dispersion term. The spatial pro...Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam （FPU） lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete fl-FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers （DBs） are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too.展开更多
The dynamics of different kinds of discrete breathers in three types of one-dimensionai monatomic chains with on-site and inter-site potentiais are investigated. The existence and evolution of symmetric breather, anti...The dynamics of different kinds of discrete breathers in three types of one-dimensionai monatomic chains with on-site and inter-site potentiais are investigated. The existence and evolution of symmetric breather, antisymmetric breather, and multibreather in one-dimensionai models are proved by using rotating wave approximation, local anharmonic approximation, and the numerical method. The linear stability of these breathers is investigated by using Lyapunov stable anaiysis. The localization and stability of breathers in three types of models correlate closely to the system nonlinear parameter β.展开更多
A general one-dimensional discrete monatomic model is investigated by using the multiple-method. It is proven that the discrete bright breathers （DBBs） and discrete dark breathers （DDBs） exist in this model at the...A general one-dimensional discrete monatomic model is investigated by using the multiple-method. It is proven that the discrete bright breathers （DBBs） and discrete dark breathers （DDBs） exist in this model at the anti-continuous limit, and then the concrete models of the DBBs and DDBs are also presented by the multiple-scale approach （MSA） and the quasi-discreteness approach （QDA）. When the results are applied to some particular models, the same conclusions as those presented in corresponding references are achieved. In addition, we use the method of the linearization analysis to investigate this system without the high order terms of ε. It is found that the DBBs and DDBs are linearly stable only when coupling parameter χ is small, of which the limited value is obtained by using an analytical method.展开更多
The modulational instability, quantum breathers and two-breathers in a frustrated easy-axis ferromagnetic zig-zag chain under an external magnetic field are investigated within the Hartree approximation. By means of a...The modulational instability, quantum breathers and two-breathers in a frustrated easy-axis ferromagnetic zig-zag chain under an external magnetic field are investigated within the Hartree approximation. By means of a linear stability analysis, we analytically study the discrete modulational instability and analyze the effect of the frustration strength on the discrete modulational instability region. Using the results from the discrete modulational instability analysis, the presence conditions of those stationary bright type localized solutions are presented. On the other hand, we obtain the analytical expressions for the stationary bright localized solutions and analyze the effect of the frustration on their emergence conditions. By taking advantage of these bright type single-magnon bound wave functions obtained, quantum breather states in the present frustrated ferromagnetic zig-zag lattice are constructed. What is more, the analytical forms for quantum two-breather states are also obtained. In particular, the energy level formulas of quantum breathers and two-breathers are derived.展开更多
We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method an...We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry＇s linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two- dimensional monatomic β-FPU lattice.展开更多
The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.However,due to the difficulty of solving this equation,in particu...The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.However,due to the difficulty of solving this equation,in particular in high dimensions,lots of methods are proposed to effectively obtain different kinds of solutions,such as neural networks among others.Recently,a method where some underlying physical laws are embeded into a conventional neural network is proposed to uncover the equation’s dynamical behaviors from spatiotemporal data directly.Compared with traditional neural networks,this method can obtain remarkably accurate solution with extraordinarily less data.Meanwhile,this method also provides a better physical explanation and generalization.In this paper,based on the above method,we present an improved deep learning method to recover the soliton solutions,breather solution,and rogue wave solutions of the nonlinear Schrodinger equation.In particular,the dynamical behaviors and error analysis about the one-order and two-order rogue waves of nonlinear integrable equations are revealed by the deep neural network with physical constraints for the first time.Moreover,the effects of different numbers of initial points sampled,collocation points sampled,network layers,neurons per hidden layer on the one-order rogue wave dynamics of this equation have been considered with the help of the control variable way under the same initial and boundary conditions.Numerical experiments show that the dynamical behaviors of soliton solutions,breather solution,and rogue wave solutions of the integrable nonlinear Schrodinger equation can be well reconstructed by utilizing this physically-constrained deep learning method.展开更多
Based on the developed Darboux transformation, we investigate the exact asymmetric solutions of breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations. As an example, some types of exact b...Based on the developed Darboux transformation, we investigate the exact asymmetric solutions of breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations. As an example, some types of exact breather solutions are given analytically by adjusting the parameters. Moreover, the interesting fundamental problem is to clarify the formation mechanism of asymmetry breather solutions and how the particle number and energy exchange between the background and soliton ultimately form the breather solutions. Our results also show that the formation mechanism from breather to rogue wave arises from the transformation from the periodic total exchange into the temporal local property.展开更多
A novel class of optical breathers, called elegant Ince-Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell＇s mode in an elliptic coordinate system, and their t...A novel class of optical breathers, called elegant Ince-Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell＇s mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear SchrSdinger equation.展开更多
The propagation properties of the breather in birefringent fibers are investigated. The breather can propagate stably in strongly birefringent fibers. The propagation law can be expected. However, random birefringence...The propagation properties of the breather in birefringent fibers are investigated. The breather can propagate stably in strongly birefringent fibers. The propagation law can be expected. However, random birefringence makes the propagation of the breather more complex. The breather will partly disappear and partly appear, even may split into two smaller breathers. In addition, the varying range of relative time displacement between two components of the breather becomes narrower with the effect of third-order dispersion. If third order dispersion is too strong, the breather behavior will disappear gradually during the transmission. The breather can exist in random birefringent fiber with dispersion management rather than in strongly birefringent fiber.展开更多
In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site pot...In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site potential and coupling potential. This study is focused on two-dimensional breathers with their frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of the existence of two-dimensional gap breathers by using a numerical method. Six types of two-dimensional gap breathers are obtained, i.e., symmetric, mirror-symmetric and asymmetric, whether the center of the breather is on a light or a heavy atom. The difference between one-dimensional discrete gap breathers and two-dimensional discrete gap breathers is also discussed. We use Aubry＇s theory to analyze the stability of discrete gap breathers in the two-dimensional diatomic face-centered square lattice.展开更多
We mainly investigate the variable-coefficient 3-coupled nonlinear Schrodinger(NLS)system,which describes soli- ton dynamics in the three-spineα-helical protein with inhomogeneous effect.The variable-coefficient NLS ...We mainly investigate the variable-coefficient 3-coupled nonlinear Schrodinger(NLS)system,which describes soli- ton dynamics in the three-spineα-helical protein with inhomogeneous effect.The variable-coefficient NLS equation is transformed into the constant coefficient NLS equation by similarity transformation firstly.The Hirota method is used to solve the constant coefficient NLS equation,and then we get the one-and two-breather solutions of the variable-coefficient NLS equation.The results show that,in the background of plane waves and periodic waves,the breather can be transformed into some forms of combined soliton solutions.The influence of different parameters on the soliton solution and the collision between two solitons are discussed by some graphs in detail.Our results are helpful to study the soliton dynamics inα-helical protein.展开更多
We derive an N-fold Darboux transformation for the nonlinear Schrdinger equation coupled to a multiple selfinduced transparency system, which is applicable to optical fiber communications in the erbium-doped medium.Th...We derive an N-fold Darboux transformation for the nonlinear Schrdinger equation coupled to a multiple selfinduced transparency system, which is applicable to optical fiber communications in the erbium-doped medium.The N-soliton, N-breather and N th-order rogue wave solutions in the compact determinant representations are derived using the Darboux transformation and limit technique. Dynamics of such solutions from the first-to second-order ones are shown.展开更多
We investigate optical superregular breathers in the femtosecond regime under dispersion management in an inho- mogeneous fiber governed by the nonautonomous higher-order nonlinear Schr6dinger equation （NLSE）. Exact...We investigate optical superregular breathers in the femtosecond regime under dispersion management in an inho- mogeneous fiber governed by the nonautonomous higher-order nonlinear Schr6dinger equation （NLSE）. Exact solutions describing the dynamics of superregular breathers are obtained. Furthermore, we discuss the propagation behaviors of controllable superregular breathers, including stabilization and recurrence in an exponential dispersion fiber and a peri- odic distributed fiber system. Particularly, the nonlinear dynamics of superregular modes evolved from an identical initial small-amplitude modulation is analyzed in detail.展开更多
Under harmonic approximation, this paper discusses the linear dispersion relation of the one-dimensional chain. The existence and evolution of discrete breathers in a general one-dimensional chain are analysed for two...Under harmonic approximation, this paper discusses the linear dispersion relation of the one-dimensional chain. The existence and evolution of discrete breathers in a general one-dimensional chain are analysed for two particular examples of soft （Morse） and hard （quartic） on-site potentials. The existence of discrete breathers in one-dimensional and two-dimensional Morse lattices is proved by using rotating wave approximation, local anharmonic approximation and a numerical method. The localization and amplitude of discrete breathers in the two-dimensional Morse lattice with on-site harmonic potentials correlate closely to the Morse parameter a and the on-site parameter к.展开更多
The discrete gap breathers （DGBs） in a one-dimensional diatomic chain with K2-K3-K4 potential are analysed. Using the local anharmonicity approximation, the analytical investigation has been implemented. The depende...The discrete gap breathers （DGBs） in a one-dimensional diatomic chain with K2-K3-K4 potential are analysed. Using the local anharmonicity approximation, the analytical investigation has been implemented. The dependence of the central amplitude of the discrete gap breathers on the breather frequency and the localization parameter are calculated. With increasing breather frequency, the DGB amplitudes decrease. As a function of the localization parameter, the central amplitude exhibits bistability, corresponding to the two branches of the curve ω = ω（ζ）. With a nonzero cubic term, the HS mode of DGB profiles becomes weaker. With increasing K3, the HS mode of DGB profiles becomes weaker and a bit narrower. For the LS mode, with increasing K3, the central particle amplitude becomes larger, and the DGB profile becomes much sharper. But, as k3 increases further, the central particle amplitude of the LS mode becomes smaller.展开更多
This paper studies a discrete one-dimensional monatomic Klein Gordon chain with only quartic nearest-neighbour interactions, in which the compact-like discrete breathers can be explicitly constructed by an exact separ...This paper studies a discrete one-dimensional monatomic Klein Gordon chain with only quartic nearest-neighbour interactions, in which the compact-like discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. Introducing the trying method, it proves that compact-like discrete breathers exist in this nonlinear system. It also discusses the linear stability of the compact-like discrete breathers, when the coefficient （β） of quartic on-site potential and the coupling constant （K4） of quartic interactive potential satisfy the given conditions, they are linearly stable.展开更多
Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein-Gordon/Fermi Pasta-Ulam diatomic chain using the expanded rotating plane-wave approxi...Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein-Gordon/Fermi Pasta-Ulam diatomic chain using the expanded rotating plane-wave approximation and numerical calculations to determine the effect of cubic potentials on the symmetry properties of discrete breathers in this system. The results will be very useful to researchers in the field of numerical calculations on discrete breathers.展开更多
基金Project supported by the the Fundamental Research Funds for the Central Universities(Grant No.2023MS163).
文摘We study a generalized higher-order nonlinear Schr¨odinger equation in an optical fiber or a planar waveguide.We obtain the Lax pair and N-fold Darboux transformation(DT)with N being a positive integer.Based on Lax pair obtained by us,we derive the infinitely-many conservation laws.We give the bright one-,two-,and N-soliton solutions,and the first-,second-,and Nth-order breather solutions based on the N-fold DT.We conclude that the velocities of the bright solitons are influenced by the distributed gain function,g(z),and variable coefficients in equation,h_(1)(z),p_(1)(z),r_(1)(z),and s_(1)(z)via the asymptotic analysis,where z represents the propagation variable or spatial coordinate.We also graphically observe that:the velocities of the first-and second-order breathers will be affected by h_(1)(z),p_(1)(z),r_(1)(z),and s_(1)(z),and the background wave depends on g(z).
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.
基金Project supported by the National Natural Science Foundation of China (Grant No 10574011)Natural Science Foundation of Heilongjiang Province,China (Grant No A200506)
文摘We study a two-dimensional （2D） diatomic lattice of anhaxmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers （DBs） can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers （QDBs） and chaotic discrete breathers （CDBs） by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.
基金supported by the National Natural Science Foundation of China(Grant No.11247255)the Natural Science Foundation of Heilongjiang Province,China(Grant No.A200506)
文摘Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam （FPU） lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete fl-FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers （DBs） are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too.
基金Supported by the National Natural Science Foundation of China under Grant No.1057411 the Foundation for Researching Group by Beijing Normal University
文摘The dynamics of different kinds of discrete breathers in three types of one-dimensionai monatomic chains with on-site and inter-site potentiais are investigated. The existence and evolution of symmetric breather, antisymmetric breather, and multibreather in one-dimensionai models are proved by using rotating wave approximation, local anharmonic approximation, and the numerical method. The linear stability of these breathers is investigated by using Lyapunov stable anaiysis. The localization and stability of breathers in three types of models correlate closely to the system nonlinear parameter β.
基金Project supported by the National Natural Science Foundation of China (Grant No 10574011)Natural Science Foundation of Heilongjiang Province,China (Grant No A200506)
文摘A general one-dimensional discrete monatomic model is investigated by using the multiple-method. It is proven that the discrete bright breathers （DBBs） and discrete dark breathers （DDBs） exist in this model at the anti-continuous limit, and then the concrete models of the DBBs and DDBs are also presented by the multiple-scale approach （MSA） and the quasi-discreteness approach （QDA）. When the results are applied to some particular models, the same conclusions as those presented in corresponding references are achieved. In addition, we use the method of the linearization analysis to investigate this system without the high order terms of ε. It is found that the DBBs and DDBs are linearly stable only when coupling parameter χ is small, of which the limited value is obtained by using an analytical method.
基金Project supported by the National Natural Science Foundation of China(Grant No.11604121)the Scientific Research Fund of Hunan Provincial Education Department,China(Grant Nos.16B210 and 16A170)the Natural Science Fund Project of Jishou University,China(Grant No.jdx17036)
文摘The modulational instability, quantum breathers and two-breathers in a frustrated easy-axis ferromagnetic zig-zag chain under an external magnetic field are investigated within the Hartree approximation. By means of a linear stability analysis, we analytically study the discrete modulational instability and analyze the effect of the frustration strength on the discrete modulational instability region. Using the results from the discrete modulational instability analysis, the presence conditions of those stationary bright type localized solutions are presented. On the other hand, we obtain the analytical expressions for the stationary bright localized solutions and analyze the effect of the frustration on their emergence conditions. By taking advantage of these bright type single-magnon bound wave functions obtained, quantum breather states in the present frustrated ferromagnetic zig-zag lattice are constructed. What is more, the analytical forms for quantum two-breather states are also obtained. In particular, the energy level formulas of quantum breathers and two-breathers are derived.
基金supported by National Natural Science Foundation of China under Grant No. 1057400the Natural Science Foundation of Heilongjiang Province under Grant No. A200506
文摘We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry＇s linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two- dimensional monatomic β-FPU lattice.
基金supported by the National Natural Science Foundation of China (Grant No. 11675054)the Fund from Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213)the Project of Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000)。
文摘The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.However,due to the difficulty of solving this equation,in particular in high dimensions,lots of methods are proposed to effectively obtain different kinds of solutions,such as neural networks among others.Recently,a method where some underlying physical laws are embeded into a conventional neural network is proposed to uncover the equation’s dynamical behaviors from spatiotemporal data directly.Compared with traditional neural networks,this method can obtain remarkably accurate solution with extraordinarily less data.Meanwhile,this method also provides a better physical explanation and generalization.In this paper,based on the above method,we present an improved deep learning method to recover the soliton solutions,breather solution,and rogue wave solutions of the nonlinear Schrodinger equation.In particular,the dynamical behaviors and error analysis about the one-order and two-order rogue waves of nonlinear integrable equations are revealed by the deep neural network with physical constraints for the first time.Moreover,the effects of different numbers of initial points sampled,collocation points sampled,network layers,neurons per hidden layer on the one-order rogue wave dynamics of this equation have been considered with the help of the control variable way under the same initial and boundary conditions.Numerical experiments show that the dynamical behaviors of soliton solutions,breather solution,and rogue wave solutions of the integrable nonlinear Schrodinger equation can be well reconstructed by utilizing this physically-constrained deep learning method.
基金Project supported by the National Natural Science Foundation of China(Grant No.61774001)the Natural Science Foundation of Hunan Province,China(Grant No.2017JJ2045)
文摘Based on the developed Darboux transformation, we investigate the exact asymmetric solutions of breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations. As an example, some types of exact breather solutions are given analytically by adjusting the parameters. Moreover, the interesting fundamental problem is to clarify the formation mechanism of asymmetry breather solutions and how the particle number and energy exchange between the background and soliton ultimately form the breather solutions. Our results also show that the formation mechanism from breather to rogue wave arises from the transformation from the periodic total exchange into the temporal local property.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11074080 and 10904041)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20094407110008)the Natural Science Foundation of Guangdong Province of China (Grant No. 10151063101000017)
文摘A novel class of optical breathers, called elegant Ince-Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell＇s mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear SchrSdinger equation.
文摘The propagation properties of the breather in birefringent fibers are investigated. The breather can propagate stably in strongly birefringent fibers. The propagation law can be expected. However, random birefringence makes the propagation of the breather more complex. The breather will partly disappear and partly appear, even may split into two smaller breathers. In addition, the varying range of relative time displacement between two components of the breather becomes narrower with the effect of third-order dispersion. If third order dispersion is too strong, the breather behavior will disappear gradually during the transmission. The breather can exist in random birefringent fiber with dispersion management rather than in strongly birefringent fiber.
基金Project supported by the National Natural Science Foundation of China (Grant No 10574011)the Foundation for Researching Group by Beijing Normal University
文摘In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site potential and coupling potential. This study is focused on two-dimensional breathers with their frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of the existence of two-dimensional gap breathers by using a numerical method. Six types of two-dimensional gap breathers are obtained, i.e., symmetric, mirror-symmetric and asymmetric, whether the center of the breather is on a light or a heavy atom. The difference between one-dimensional discrete gap breathers and two-dimensional discrete gap breathers is also discussed. We use Aubry＇s theory to analyze the stability of discrete gap breathers in the two-dimensional diatomic face-centered square lattice.
基金supported by the Scientific and Technological Innovation Programs of Higher Education Institution in Shanxi,China(Grant Nos.2020L0525 and 2019L0782)the National Natural Science Foundation of China(Grant Nos.11805141 and 12075210)+2 种基金Applied Basic Research Program of Shanxi Province,China(Grant No.201901D211424)“1331 Project”Key Innovative Research Team of Taiyuan Normal University(Grant No.I0190364)Key Research and Development program of Shanxi Province,China(Grant No.201903D421042).
文摘We mainly investigate the variable-coefficient 3-coupled nonlinear Schrodinger(NLS)system,which describes soli- ton dynamics in the three-spineα-helical protein with inhomogeneous effect.The variable-coefficient NLS equation is transformed into the constant coefficient NLS equation by similarity transformation firstly.The Hirota method is used to solve the constant coefficient NLS equation,and then we get the one-and two-breather solutions of the variable-coefficient NLS equation.The results show that,in the background of plane waves and periodic waves,the breather can be transformed into some forms of combined soliton solutions.The influence of different parameters on the soliton solution and the collision between two solitons are discussed by some graphs in detail.Our results are helpful to study the soliton dynamics inα-helical protein.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11705290 and 11305060the China Postdoctoral Science Foundation under Grant No 2016M602252
文摘We derive an N-fold Darboux transformation for the nonlinear Schrdinger equation coupled to a multiple selfinduced transparency system, which is applicable to optical fiber communications in the erbium-doped medium.The N-soliton, N-breather and N th-order rogue wave solutions in the compact determinant representations are derived using the Darboux transformation and limit technique. Dynamics of such solutions from the first-to second-order ones are shown.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11547302,11705145,and 11434013)
文摘We investigate optical superregular breathers in the femtosecond regime under dispersion management in an inho- mogeneous fiber governed by the nonautonomous higher-order nonlinear Schr6dinger equation （NLSE）. Exact solutions describing the dynamics of superregular breathers are obtained. Furthermore, we discuss the propagation behaviors of controllable superregular breathers, including stabilization and recurrence in an exponential dispersion fiber and a peri- odic distributed fiber system. Particularly, the nonlinear dynamics of superregular modes evolved from an identical initial small-amplitude modulation is analyzed in detail.
基金supported by the National Natural Science Foundation of China (Grant No. 1057411)the Foundation for Researching Group by Beijing Normal University
文摘Under harmonic approximation, this paper discusses the linear dispersion relation of the one-dimensional chain. The existence and evolution of discrete breathers in a general one-dimensional chain are analysed for two particular examples of soft （Morse） and hard （quartic） on-site potentials. The existence of discrete breathers in one-dimensional and two-dimensional Morse lattices is proved by using rotating wave approximation, local anharmonic approximation and a numerical method. The localization and amplitude of discrete breathers in the two-dimensional Morse lattice with on-site harmonic potentials correlate closely to the Morse parameter a and the on-site parameter к.
基金Project supported by the National Natural Science Foundation of China （Grant No 10574011）.
文摘The discrete gap breathers （DGBs） in a one-dimensional diatomic chain with K2-K3-K4 potential are analysed. Using the local anharmonicity approximation, the analytical investigation has been implemented. The dependence of the central amplitude of the discrete gap breathers on the breather frequency and the localization parameter are calculated. With increasing breather frequency, the DGB amplitudes decrease. As a function of the localization parameter, the central amplitude exhibits bistability, corresponding to the two branches of the curve ω = ω（ζ）. With a nonzero cubic term, the HS mode of DGB profiles becomes weaker. With increasing K3, the HS mode of DGB profiles becomes weaker and a bit narrower. For the LS mode, with increasing K3, the central particle amplitude becomes larger, and the DGB profile becomes much sharper. But, as k3 increases further, the central particle amplitude of the LS mode becomes smaller.
基金Project supported by the National Natural Science Foundation of China (Grant No 10574011)Natural Science Foundation of Heilongjiang Province, China (Grant No A200506)
文摘This paper studies a discrete one-dimensional monatomic Klein Gordon chain with only quartic nearest-neighbour interactions, in which the compact-like discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. Introducing the trying method, it proves that compact-like discrete breathers exist in this nonlinear system. It also discusses the linear stability of the compact-like discrete breathers, when the coefficient （β） of quartic on-site potential and the coupling constant （K4） of quartic interactive potential satisfy the given conditions, they are linearly stable.
基金Project supported by the National Natural Science Foundation of China (Grant No.10574011)the Foundation for Innovative Research Groups Foundation of Beijing Normal University
文摘Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein-Gordon/Fermi Pasta-Ulam diatomic chain using the expanded rotating plane-wave approximation and numerical calculations to determine the effect of cubic potentials on the symmetry properties of discrete breathers in this system. The results will be very useful to researchers in the field of numerical calculations on discrete breathers.
