In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equat...In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.展开更多
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie gr...The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.展开更多
A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the solito...A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.展开更多
In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the ...In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.展开更多
This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time- delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative ro...This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time- delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1：1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.展开更多
Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite differ...Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.展开更多
The fractional quadric-cubic coupled nonlinear Schrodinger equation is concerned,and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method.The relationship between the Lé...The fractional quadric-cubic coupled nonlinear Schrodinger equation is concerned,and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method.The relationship between the Lévy index and the amplitudes of vector symmetric and antisymmetric solitons is investigated.Two components of vector symmetric and antisymmetric solitons show a positive and negative trend with the Lévy index,respectively.The stability intervals of these solitons and the propagation constants corresponding to the maximum and minimum instability growth rates are studied.Results indicate that vector symmetric solitons are more stable and have better interference resistance than vector antisymmetric solitons.展开更多
In this work, we will derive numerical schemes for solving 3-coupled nonlinear Schrödinger equations using finite difference method and time splitting method combined with finite difference method. The result...In this work, we will derive numerical schemes for solving 3-coupled nonlinear Schrödinger equations using finite difference method and time splitting method combined with finite difference method. The resulting schemes are highly accurate, unconditionally stable. We use the exact single soliton solution and the conserved quantities to check the accuracy and the efficiency of the proposed schemes. Also, we use these methods to study the interaction dynamics of two solitons. It is found that both elastic and inelastic collision can take place under suitable parametric conditions. We have noticed that the inelastic collision of single solitons occurs in two different manners: enhancement or suppression of the amplitude.展开更多
Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifie...Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-Ⅰ and type-Ⅱ rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue waves.When the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively.展开更多
We use the Lagrangian perturbation method to investigate the properties of soliton solutions in the coupled nonlinear Schrödinger equations subject to weak dissipation.Our study reveals that the two-component sol...We use the Lagrangian perturbation method to investigate the properties of soliton solutions in the coupled nonlinear Schrödinger equations subject to weak dissipation.Our study reveals that the two-component soliton solutions act as fixed-point attractors,where the numerical evolution of the system always converges to a soliton solution,regardless of the initial conditions.Interestingly,the fixed-point attractor appears as a soliton solution with a constant sum of the two-component intensities and a fixed soliton velocity,but each component soliton does not exhibit the attractor feature if the dissipation terms are identical.This suggests that one soliton attractor in the coupled systems can correspond to a group of soliton solutions,which is different from scalar cases.Our findings could inspire further discussions on dissipative-soliton dynamics in coupled systems.展开更多
This study successfully reveals the dark,singular solitons,periodic wave and singular periodic wave solutions of the(1+1)-dimensional coupled nonlinear Schr?dinger equation by using the extended rational sine-cosine a...This study successfully reveals the dark,singular solitons,periodic wave and singular periodic wave solutions of the(1+1)-dimensional coupled nonlinear Schr?dinger equation by using the extended rational sine-cosine and rational sinh-cosh methods.The modulation instability analysis of the governing model is presented.By using the suitable values of the parameters involved,the 2-,3-dimensional and the contour graphs of some of the reported solutions are plotted.展开更多
Based on the generalized coupled nonlinear Schr¨odinger equation,we obtain the analytic four-bright–bright soliton solution by using the Hirota bilinear method.The interactions among four solitons are also studi...Based on the generalized coupled nonlinear Schr¨odinger equation,we obtain the analytic four-bright–bright soliton solution by using the Hirota bilinear method.The interactions among four solitons are also studied in detail.The results show that the interaction among four solitons mainly depends on the values of solution parameters;k1 and k2 mainly affect the two inboard solitons while k3 and k4 mainly affect the two outboard solitons;the pulse velocity and width mainly depend on the imaginary part of ki(i=1,2,3,4),while the pulse amplitude mainly depends on the real part of ki(i=1,2,3,4).展开更多
The Painleve integrability and exact solutions to a coupled nonlinear Schrodinger （CNLS） equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass th...The Painleve integrability and exact solutions to a coupled nonlinear Schrodinger （CNLS） equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painleve test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.展开更多
In this paper we are going to derive two numerical methods for solving the coupled nonlinear Schrodinger-Boussinesq equation. The first method is a nonlinear implicit scheme of second order accuracy in both directions...In this paper we are going to derive two numerical methods for solving the coupled nonlinear Schrodinger-Boussinesq equation. The first method is a nonlinear implicit scheme of second order accuracy in both directions time and space;the scheme is unconditionally stable. The second scheme is a nonlinear implicit scheme of second order accuracy in time and fourth order accuracy in space direction. A generalized method is also derived where the previous schemes can be obtained by some special values of l. The proposed methods will produced a coupled nonlinear tridiagonal system which can be solved by fixed point method. The exact solutions and the conserved quantities for two different tests are used to display the robustness of the proposed schemes.展开更多
We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,...We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.展开更多
With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have pot...With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems （i.e. Lax pair）, we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers.展开更多
With the rapid development of communication technology,optical fiber communication has become a key research area in communications.When there are two signals in the optical fiber,the transmission of them can be abstr...With the rapid development of communication technology,optical fiber communication has become a key research area in communications.When there are two signals in the optical fiber,the transmission of them can be abstracted as a high-order coupled nonlinear Schr¨odinger system.In this paper,by using the Hirota’s method,we construct the bilinear forms,and study the analytical solution of three solitons in the case of focusing interactions.In addition,by adjusting different wave numbers for phase control,we further discuss the influence of wave numbers on soliton transmissions.It is verified that wave numbers k_(11),k_(21),k_(31),k_(22),and k_(32)can control the fusion and fission of solitons.The results are beneficial to the study of all-optical switches and fiber lasers in nonlinear optics.展开更多
The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was...The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the singular perturbation theory and the fixed-point argument.展开更多
We construct various novel exact solutions of two coupled dynamical nonlinear Schrōdinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrōdinger equations with time-and space-...We construct various novel exact solutions of two coupled dynamical nonlinear Schrōdinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrōdinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrrdinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.展开更多
In this work, we present the direct discontinuous Galerkin （DDG） method for the one-dimensional coupled nonlinear Schr5dinger （CNLS） equation. We prove that the new discontinuous Galerkin method preserves the disc...In this work, we present the direct discontinuous Galerkin （DDG） method for the one-dimensional coupled nonlinear Schr5dinger （CNLS） equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.展开更多
文摘In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.
基金supported by the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institutethe National Natural Science Foundation of China under Grant Nos. 10735030 and 90503006
文摘The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.
基金Project supported by the National Natural Science Foundation of China(Grant No.11161017)the National Science Foundation of Hainan Province,China(Grant No.113001)
文摘A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.
基金Project supported by the National Natural Science Foundation of China （Grant No 10575087） and the Natural Science Foundation of Zheiiang Province of China （Grant No 102053）. 0ne of the authors （Lin） would like to thank Prof. Sen-yue Lou for many useful discussions.
文摘In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.
基金Project supported by the National Natural Science Foundation of China(Grant No.61104040)the Natural Science Foundation of Hebei Province,China(Grant No.E2012203090)
文摘This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time- delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1：1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.
基金Supported by the National Natural Science Foundation of China under Grant No.91130013Hunan Provincial Innovation Foundation under Grant No.CX2012B010+1 种基金the Innovation Fund of National University of Defense Technology under Grant No.B120205the Open Foundation of State Key Laboratory
文摘Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.
基金supported by Zhejiang Provincial Natural Science Foundation of China(No.LR20A050001)National Natural Science Foundation of China(No.12075210)the Scientific Research and Developed Fund of Zhejiang A&F University(Grant No.2021FR0009)。
文摘The fractional quadric-cubic coupled nonlinear Schrodinger equation is concerned,and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method.The relationship between the Lévy index and the amplitudes of vector symmetric and antisymmetric solitons is investigated.Two components of vector symmetric and antisymmetric solitons show a positive and negative trend with the Lévy index,respectively.The stability intervals of these solitons and the propagation constants corresponding to the maximum and minimum instability growth rates are studied.Results indicate that vector symmetric solitons are more stable and have better interference resistance than vector antisymmetric solitons.
文摘In this work, we will derive numerical schemes for solving 3-coupled nonlinear Schrödinger equations using finite difference method and time splitting method combined with finite difference method. The resulting schemes are highly accurate, unconditionally stable. We use the exact single soliton solution and the conserved quantities to check the accuracy and the efficiency of the proposed schemes. Also, we use these methods to study the interaction dynamics of two solitons. It is found that both elastic and inelastic collision can take place under suitable parametric conditions. We have noticed that the inelastic collision of single solitons occurs in two different manners: enhancement or suppression of the amplitude.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11772017,11272023,and 11471050the Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications),China(IPOC:2017ZZ05)the Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02
文摘Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-Ⅰ and type-Ⅱ rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue waves.When the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively.
基金supported by the National Natural Science Foundation of China(Contract No.12022513,12235007)the Major Basic Research Program of Natural Science of Shaanxi Province(Grant No.2018KJXX-094)
文摘We use the Lagrangian perturbation method to investigate the properties of soliton solutions in the coupled nonlinear Schrödinger equations subject to weak dissipation.Our study reveals that the two-component soliton solutions act as fixed-point attractors,where the numerical evolution of the system always converges to a soliton solution,regardless of the initial conditions.Interestingly,the fixed-point attractor appears as a soliton solution with a constant sum of the two-component intensities and a fixed soliton velocity,but each component soliton does not exhibit the attractor feature if the dissipation terms are identical.This suggests that one soliton attractor in the coupled systems can correspond to a group of soliton solutions,which is different from scalar cases.Our findings could inspire further discussions on dissipative-soliton dynamics in coupled systems.
文摘This study successfully reveals the dark,singular solitons,periodic wave and singular periodic wave solutions of the(1+1)-dimensional coupled nonlinear Schr?dinger equation by using the extended rational sine-cosine and rational sinh-cosh methods.The modulation instability analysis of the governing model is presented.By using the suitable values of the parameters involved,the 2-,3-dimensional and the contour graphs of some of the reported solutions are plotted.
基金National Natural Science Foundation of China(Grant No.11705108).
文摘Based on the generalized coupled nonlinear Schr¨odinger equation,we obtain the analytic four-bright–bright soliton solution by using the Hirota bilinear method.The interactions among four solitons are also studied in detail.The results show that the interaction among four solitons mainly depends on the values of solution parameters;k1 and k2 mainly affect the two inboard solitons while k3 and k4 mainly affect the two outboard solitons;the pulse velocity and width mainly depend on the imaginary part of ki(i=1,2,3,4),while the pulse amplitude mainly depends on the real part of ki(i=1,2,3,4).
基金Project supported by the National Natural Science Foundation of China (Nos. 10735030and 40775069)the Natural Science Foundation of Guangdong Province of China(No. 10452840301004616)the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute (No. 408YKQ09)
文摘The Painleve integrability and exact solutions to a coupled nonlinear Schrodinger （CNLS） equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painleve test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.
文摘In this paper we are going to derive two numerical methods for solving the coupled nonlinear Schrodinger-Boussinesq equation. The first method is a nonlinear implicit scheme of second order accuracy in both directions time and space;the scheme is unconditionally stable. The second scheme is a nonlinear implicit scheme of second order accuracy in time and fourth order accuracy in space direction. A generalized method is also derived where the previous schemes can be obtained by some special values of l. The proposed methods will produced a coupled nonlinear tridiagonal system which can be solved by fixed point method. The exact solutions and the conserved quantities for two different tests are used to display the robustness of the proposed schemes.
基金Project supported by the Global Change Research Program of China(Grant No.2015CB953904)the National Natural Science Foundation of China(Grant Nos.11275072 and 11435005)+2 种基金the Doctoral Program of Higher Education of China(Grant No.20120076110024)the Network Information Physics Calculation of Basic Research Innovation Research Group of China(Grant No.61321064)Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things,China(Grant No.ZF1213)
文摘We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.
基金Supported by the National Natural Science Foundation of China under Grant No.60772023 the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.BUAA-SKLSDE-09KF-04+2 种基金Beijing University of Aeronautics and Astronautics,by the National Basic Research Program of China (973 Program) under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos.20060006024 and 200800130006Chinese Ministry of Education
文摘With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems （i.e. Lax pair）, we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers.
基金supported by the National Natural Science Foundation of China(Grant Nos.11875008,12075034,11975001,and 11975172)the Open Research Fund of State Key Laboratory of Pulsed Power Laser Technology(Grant No.SKL2018KF04)the Fundamental Research Funds for the Central Universities,China(Grant No.2019XD-A09-3)。
文摘With the rapid development of communication technology,optical fiber communication has become a key research area in communications.When there are two signals in the optical fiber,the transmission of them can be abstracted as a high-order coupled nonlinear Schr¨odinger system.In this paper,by using the Hirota’s method,we construct the bilinear forms,and study the analytical solution of three solitons in the case of focusing interactions.In addition,by adjusting different wave numbers for phase control,we further discuss the influence of wave numbers on soliton transmissions.It is verified that wave numbers k_(11),k_(21),k_(31),k_(22),and k_(32)can control the fusion and fission of solitons.The results are beneficial to the study of all-optical switches and fiber lasers in nonlinear optics.
文摘The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the singular perturbation theory and the fixed-point argument.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11275072,11075055,and 11271211)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120076110024)+3 种基金the Innovative Research Team Program of the National Natural Science Foundation of China(Grant No.61021004)the Shanghai Leading Academic Discipline Project,China(Grant No.B412)the National High Technology Research and Development Program of China(Grant No.2011AA010101)the Shanghai Knowledge Service Platform for Trustworthy Internet of Things,China(Grant No.ZF1213)
文摘We construct various novel exact solutions of two coupled dynamical nonlinear Schrōdinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrōdinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrrdinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.
基金Project supported by the National Natural Science Foundation of China （Grant No 11171038）.
文摘In this work, we present the direct discontinuous Galerkin （DDG） method for the one-dimensional coupled nonlinear Schr5dinger （CNLS） equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.
