A unified theoretical aeroservoelastic stability analysis framework for flexible aircraft is established in this paper. This linearized state space model for stability analysis is based on nonlinear coupled dynamic eq...A unified theoretical aeroservoelastic stability analysis framework for flexible aircraft is established in this paper. This linearized state space model for stability analysis is based on nonlinear coupled dynamic equations, in which rigid and elastic motions of aircraft are both considered.The common body coordinate system is utilized as the reference frame in the deduction of dynamic equations, and significant deformations of flexible aircraft are also fully concerned without any excessive assumptions. Therefore, the obtained nonlinear coupled dynamic models can well reflect the special dynamic coupling mechanics of flexible aircraft. For aeroservoelastic stability analysis,the coupled dynamic equations are linearized around the nonlinear equilibrium state and together with a control system model to establish a state space model in the time domain. The methodology in this paper can be easily integrated into the industrial design process and complex structures.Numerical results for a complex flexible aircraft indicate the necessity to consider the nonlinear coupled dynamics and large deformation when dealing with aeroservoelastic stability for flexible aircraft.展开更多
To predict aeroheating performance of hypersonic vehicles accurately in thermochemical nonequilibrium flows accompanied by rarefaction effect,a Nonlinear Coupled Constitutive Relations(NCCR)model coupled with Gupta’s...To predict aeroheating performance of hypersonic vehicles accurately in thermochemical nonequilibrium flows accompanied by rarefaction effect,a Nonlinear Coupled Constitutive Relations(NCCR)model coupled with Gupta’s chemical models and Park’s two-temperature model is firstly proposed in this paper.Three typical cases are intensively investigated for further validation,including hypersonic flows over a two-dimensional cylinder,a RAM-C II flight vehicle and a type HTV-2 flight vehicle.The results predicted by NCCR solution,such as heat flux coefficient and electron number densities,are in better agreement with those of direct simulation Monte Carlo or flight data than Navier-Stokes equations,especially in the extremely nonequilibrium regions,which indicates the potential of the newly-developed solution to capture both thermochemical and rarefied nonequilibrium effects.The comparisons between the present solver and NCCR model without a two-temperature model are also conducted to demonstrate the significance of vibrational energy source term in the accurate simulation of high-Mach flows.展开更多
We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node. Both delay coupling and non-delay coupling, as well as the symmetrical coupling matrix and the asymmetrical coupli...We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node. Both delay coupling and non-delay coupling, as well as the symmetrical coupling matrix and the asymmetrical coupling matrix are considered. Based on the comparison theorem of an impulsive differential system, some novel synchronization criteria are derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.展开更多
By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions ...By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.展开更多
Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ^4 model are presented. Simultaneously, inspired by the new solutions of the famous φ^4 model recently proposed by J...Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ^4 model are presented. Simultaneously, inspired by the new solutions of the famous φ^4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scaiar field （NCSF） system are obtained.展开更多
In this paper, the problem of initial boundary value for nonlinear coupled reaction-diffusion systems arising in biochemistry, engineering and combustion_theory is considered.
A dynamic response analysis of tension leg platform (TLP) to deterministic first order wave forces is presented, considering coupling between various degrees of freedom surge, sway, heave, pitch, roll and yaw. The ana...A dynamic response analysis of tension leg platform (TLP) to deterministic first order wave forces is presented, considering coupling between various degrees of freedom surge, sway, heave, pitch, roll and yaw. The analysis duly considers nonlinearities produced due to changes in cable-tension and due to nonlinear hydro-dynamic drag forces. The wave forces on the elements of the pontoon structure are calculated using Airy's wave theory and Morison's equation. The nonlinear equation of motion is solved in the time domain by Newmark's β-method. With the help of proposed analysis, some example problems are solved in order to investigate the effects of different important factors that influence the response of TLP.展开更多
Considering the static stability and the change of the displacement volume, including the influences of higher order nonlinear terms and the instantaneous wave surface, the nonlinear coupled heave-pitch motion was est...Considering the static stability and the change of the displacement volume, including the influences of higher order nonlinear terms and the instantaneous wave surface, the nonlinear coupled heave-pitch motion was established in stochastic waves. The responses of heave-pitch coupling motion for the Truss Spar platform were investigated. It was found that, when the characteristic frequency of a stochastic wave is close to the natural heave frequency, the large amplitude pitch motion is induced under the parametric-forced excitation, which is called the Mathieu instability. It was observed that the heave mode energy is transferred to pitch mode when the heave motion amplitude exceeds a certain extent. In addition, the probability of internal resonant heave-pitch motion is greatly reduced while the characteristic wave frequency is away from the natural heave frequency.展开更多
More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance m...More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.展开更多
The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
Dear Editor,This letter studies the event-triggered adaptive horizon distributed model predictive control problem for discrete-time coupled nonlinear systems with additive disturbances.By constructing a new dualmodel ...Dear Editor,This letter studies the event-triggered adaptive horizon distributed model predictive control problem for discrete-time coupled nonlinear systems with additive disturbances.By constructing a new dualmodel optimal control problem,an event-triggered mechanism and an adaptive prediction horizon scheme are co-designed in the proposed scheme.Notably,the upper bound of the triggering interval remains independent of the dynamically shrinking prediction horizon.This enables the event-triggered mechanism to operate effectively even when the prediction horizon becomes zero,thus achieving cost savings throughout the control process.In addition,the sufficient conditions of the proposed scheme associated with the feasibility and stability are provided.The effectiveness is illustrated through a practical example.展开更多
Shock tunnels are indispensable facilities for hypersonic aerodynamic experimentation.Within these systems,the diaphragm plays a pivotal role,as its rupture process critically influences shock wave generation quality,...Shock tunnels are indispensable facilities for hypersonic aerodynamic experimentation.Within these systems,the diaphragm plays a pivotal role,as its rupture process critically influences shock wave generation quality,experimental repeatability,and facility reliability.A thorough understanding of diaphragm rupture dynamics is therefore essential for optimizing shock tunnel design,improving experimental accuracy,and ensuring operational safety.To address the complex challenge of fully coupled multiphysics analysis in high-pressure-ratio shock tunnels,this study introduces a high-fidelity,three-dimensional,fully coupled Fluid-Structure Interaction(FSI)simulation framework.This framework seamlessly integrates the Dual Conservation Element and Solution Element(Dual-CESE)method,the Immersed Boundary Method(IBM),and the JohnsonCook(J-C)material constitutive and failure model.The combined approach enables synchronized simulation and analysis of the entire diaphragm rupture sequence—including pre-deformation,crack initiation and propagation,and fully developed petaling deformation—alongside the formation and evolution of the associated supersonic flow field.The simulation results show strong agreement with experimental observations,with the post-rupture geometric morphology accurately replicated and a shock wave velocity deviation of only 2.55%from experimental measurements.The study uncovers the dynamic failure mechanisms,revealing that nonlinear pressure loading initiates cracking within the diaphragm.It further elucidates how the nonlinearly coupled interactions between petaling dynamics and fracture morphology directly impact shock wave formation and evolution.This computational framework provides a novel and robust methodology for advancing shock tunnel design and conducting comprehensive reliability assessments.展开更多
The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown th...The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.展开更多
In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)...In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)+Dt^(2))by using the error splitting technique and postprocessing interpolation.Numerical experiments are carried out to support our theoretical results.展开更多
The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate t...The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate tothe envelope shock wave solutions and/or the envelope solitary wave solutions.展开更多
We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured b...We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured by a fractional differential operator, which is defined in the Riemann-Liouville sense, and a nonlinear term in which different solution components are coupled. The analysis is based on the reduction of the given system to an equivalent system of integral equations. By means of the nonlinear alternative of Leray-Schauder,the existence of solutions of the factional differential system is obtained. The uniqueness is established by using the Banach contraction principle.展开更多
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
基金supported by the National Key Research and Development Program of China(No.2016YFB0200703)
文摘A unified theoretical aeroservoelastic stability analysis framework for flexible aircraft is established in this paper. This linearized state space model for stability analysis is based on nonlinear coupled dynamic equations, in which rigid and elastic motions of aircraft are both considered.The common body coordinate system is utilized as the reference frame in the deduction of dynamic equations, and significant deformations of flexible aircraft are also fully concerned without any excessive assumptions. Therefore, the obtained nonlinear coupled dynamic models can well reflect the special dynamic coupling mechanics of flexible aircraft. For aeroservoelastic stability analysis,the coupled dynamic equations are linearized around the nonlinear equilibrium state and together with a control system model to establish a state space model in the time domain. The methodology in this paper can be easily integrated into the industrial design process and complex structures.Numerical results for a complex flexible aircraft indicate the necessity to consider the nonlinear coupled dynamics and large deformation when dealing with aeroservoelastic stability for flexible aircraft.
基金financially co-supported by the National Natural Science Foundation of China(Nos.12002306,U20B2007,11572284 and 6162790014)National Numerical Wind Tunnel Project,China(No.NNW2019ZT3-A08)。
文摘To predict aeroheating performance of hypersonic vehicles accurately in thermochemical nonequilibrium flows accompanied by rarefaction effect,a Nonlinear Coupled Constitutive Relations(NCCR)model coupled with Gupta’s chemical models and Park’s two-temperature model is firstly proposed in this paper.Three typical cases are intensively investigated for further validation,including hypersonic flows over a two-dimensional cylinder,a RAM-C II flight vehicle and a type HTV-2 flight vehicle.The results predicted by NCCR solution,such as heat flux coefficient and electron number densities,are in better agreement with those of direct simulation Monte Carlo or flight data than Navier-Stokes equations,especially in the extremely nonequilibrium regions,which indicates the potential of the newly-developed solution to capture both thermochemical and rarefied nonequilibrium effects.The comparisons between the present solver and NCCR model without a two-temperature model are also conducted to demonstrate the significance of vibrational energy source term in the accurate simulation of high-Mach flows.
基金Project supported by the Young Project of Hubei Provincial Department of Education,China(Grant No.Q20111309)the Key Program of Hubei Provincial Department of Education,China(Grant No.D20101304)
文摘We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node. Both delay coupling and non-delay coupling, as well as the symmetrical coupling matrix and the asymmetrical coupling matrix are considered. Based on the comparison theorem of an impulsive differential system, some novel synchronization criteria are derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.
文摘By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.
基金National Natural Science Foundation of China under Grant Nos.10475055 and 90503006the Scientific Research Fund of the Education Department of Zhejiang Province under Grant No.20040969
文摘Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ^4 model are presented. Simultaneously, inspired by the new solutions of the famous φ^4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scaiar field （NCSF） system are obtained.
文摘In this paper, the problem of initial boundary value for nonlinear coupled reaction-diffusion systems arising in biochemistry, engineering and combustion_theory is considered.
文摘A dynamic response analysis of tension leg platform (TLP) to deterministic first order wave forces is presented, considering coupling between various degrees of freedom surge, sway, heave, pitch, roll and yaw. The analysis duly considers nonlinearities produced due to changes in cable-tension and due to nonlinear hydro-dynamic drag forces. The wave forces on the elements of the pontoon structure are calculated using Airy's wave theory and Morison's equation. The nonlinear equation of motion is solved in the time domain by Newmark's β-method. With the help of proposed analysis, some example problems are solved in order to investigate the effects of different important factors that influence the response of TLP.
基金Supported by the National Natural Science Foundation of China(No. 51079097, 50879057)
文摘Considering the static stability and the change of the displacement volume, including the influences of higher order nonlinear terms and the instantaneous wave surface, the nonlinear coupled heave-pitch motion was established in stochastic waves. The responses of heave-pitch coupling motion for the Truss Spar platform were investigated. It was found that, when the characteristic frequency of a stochastic wave is close to the natural heave frequency, the large amplitude pitch motion is induced under the parametric-forced excitation, which is called the Mathieu instability. It was observed that the heave mode energy is transferred to pitch mode when the heave motion amplitude exceeds a certain extent. In addition, the probability of internal resonant heave-pitch motion is greatly reduced while the characteristic wave frequency is away from the natural heave frequency.
文摘More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
基金supported by the National Natural Science Foundation of China(62473265,62476176,12426311).
文摘Dear Editor,This letter studies the event-triggered adaptive horizon distributed model predictive control problem for discrete-time coupled nonlinear systems with additive disturbances.By constructing a new dualmodel optimal control problem,an event-triggered mechanism and an adaptive prediction horizon scheme are co-designed in the proposed scheme.Notably,the upper bound of the triggering interval remains independent of the dynamically shrinking prediction horizon.This enables the event-triggered mechanism to operate effectively even when the prediction horizon becomes zero,thus achieving cost savings throughout the control process.In addition,the sufficient conditions of the proposed scheme associated with the feasibility and stability are provided.The effectiveness is illustrated through a practical example.
基金supported by the National Key R&D Program of China(No.2021YFC3100700)。
文摘Shock tunnels are indispensable facilities for hypersonic aerodynamic experimentation.Within these systems,the diaphragm plays a pivotal role,as its rupture process critically influences shock wave generation quality,experimental repeatability,and facility reliability.A thorough understanding of diaphragm rupture dynamics is therefore essential for optimizing shock tunnel design,improving experimental accuracy,and ensuring operational safety.To address the complex challenge of fully coupled multiphysics analysis in high-pressure-ratio shock tunnels,this study introduces a high-fidelity,three-dimensional,fully coupled Fluid-Structure Interaction(FSI)simulation framework.This framework seamlessly integrates the Dual Conservation Element and Solution Element(Dual-CESE)method,the Immersed Boundary Method(IBM),and the JohnsonCook(J-C)material constitutive and failure model.The combined approach enables synchronized simulation and analysis of the entire diaphragm rupture sequence—including pre-deformation,crack initiation and propagation,and fully developed petaling deformation—alongside the formation and evolution of the associated supersonic flow field.The simulation results show strong agreement with experimental observations,with the post-rupture geometric morphology accurately replicated and a shock wave velocity deviation of only 2.55%from experimental measurements.The study uncovers the dynamic failure mechanisms,revealing that nonlinear pressure loading initiates cracking within the diaphragm.It further elucidates how the nonlinearly coupled interactions between petaling dynamics and fracture morphology directly impact shock wave formation and evolution.This computational framework provides a novel and robust methodology for advancing shock tunnel design and conducting comprehensive reliability assessments.
文摘The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.
基金The work is supported by the National Natural Science Foundation of China(No.11871441)Beijing Natural Science Foundation(No.1192003).
文摘In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)+Dt^(2))by using the error splitting technique and postprocessing interpolation.Numerical experiments are carried out to support our theoretical results.
文摘The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate tothe envelope shock wave solutions and/or the envelope solitary wave solutions.
基金supported by National Natural Science Foundation of China(Grant Nos.11471274,11421110001 and 91130002)Natural Science Foundation of Guizhou Province(Grant No.LKS[2013]04)
文摘We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured by a fractional differential operator, which is defined in the Riemann-Liouville sense, and a nonlinear term in which different solution components are coupled. The analysis is based on the reduction of the given system to an equivalent system of integral equations. By means of the nonlinear alternative of Leray-Schauder,the existence of solutions of the factional differential system is obtained. The uniqueness is established by using the Banach contraction principle.
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.
