Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the co...Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics.展开更多
Searching for special solitary wave solutions with compact support is of important significance in soliton theory. In this paper, to understand the role of nonlinear dispersion in pattern formation, a family of the re...Searching for special solitary wave solutions with compact support is of important significance in soliton theory. In this paper, to understand the role of nonlinear dispersion in pattern formation, a family of the regularized long-wave Boussinesq equations with fully nonlinear dispersion (simply called equations), ( const.), is studied. New solitary wave solutions with compact support of equations are found. In addition we find another compacton solutions of the two special cases, equation and equation. It is found that the nonlinear dispersion term in a nonlinear evolution equation is not a necessary condition of that it possesses compacton solutions.展开更多
In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well...In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations.展开更多
An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed. The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system...An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed. The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system and constructs an iteration algorithm to generate the monotone sequence. The convergence of the algorithm for nonlinear discrete Hamilton-Jacobi-Bellman equations is proved. Some numerical examples are presented to confirm the effciency of this algorithm.展开更多
Based on the modified mixed Hellinger-Reissner（H-R） variational principle for elastic bodies with damping, the state-vector equation with parameters is directionally derived from the principle. A new solution for th...Based on the modified mixed Hellinger-Reissner（H-R） variational principle for elastic bodies with damping, the state-vector equation with parameters is directionally derived from the principle. A new solution for the harmonic vibration of simply supported rectangular laminates with damping is proposed by using the precise integration method and Muller method. The general solutions for the free vibration of underdamping, critical damp and overdamping of composite laminates are given simply in terms of the linear damping vibration theory. The effect of viscous damping force on the vibration of composite laminates is investigated through numerical examples. The state-vector equation theory and its application areas are extended.展开更多
Deals with the application of Kreiss resolvent condition in the error growth analysis of numerical methods, and studies the stability of Runge Kutta method in respect of Kreiss resolvent condition with emphasis on the...Deals with the application of Kreiss resolvent condition in the error growth analysis of numerical methods, and studies the stability of Runge Kutta method in respect of Kreiss resolvent condition with emphasis on the study on the subclass of collocation methods with abscissas in [0,1] by applying the methods to the test equation U′(t)=λU(t)+μU(t-τ)τ>0 with complex constraints μ and λ, and proves under some assumptions on the R K methods that the error growth is uniformly bounded in the stability region.展开更多
In this paper, we establish exact solutions for the .R（m,n） equations by using an sn-cn metnou,As a result, abundant new cornpactons, i,e, solitons with the absence of infinite wings, new type of Jacobi elliptic fun...In this paper, we establish exact solutions for the .R（m,n） equations by using an sn-cn metnou,As a result, abundant new cornpactons, i,e, solitons with the absence of infinite wings, new type of Jacobi elliptic function, solitary wave and periodic wave solutions, of this equation are obtained with minimal calculations. The properties of the R（m, n） equations are shown in figures.展开更多
A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the pro...A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the process are Boolean functions, the optimal control problem related to the process can be solved by relating between the transfer functions and the objective functional. An analogue of Bellman function for the optimal control problem mentioned is defined and consequently suitable Bellman equation is constructed.展开更多
In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the me...In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.展开更多
The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-s...The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.展开更多
This paper presents a modified domain decomposition method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal control problems using diffusion models. A convergenc...This paper presents a modified domain decomposition method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal control problems using diffusion models. A convergence theorem is established. Numerical results indicate the effectiveness and accuracy of the method.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.12071042)Beijing Natural Science Foundation (Grant No.1202006)。
文摘Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics.
基金National Key Basic Research Development Project Program of China under Grant，Doctoral Foundation of China under Grant，国家自然科学基金
文摘Searching for special solitary wave solutions with compact support is of important significance in soliton theory. In this paper, to understand the role of nonlinear dispersion in pattern formation, a family of the regularized long-wave Boussinesq equations with fully nonlinear dispersion (simply called equations), ( const.), is studied. New solitary wave solutions with compact support of equations are found. In addition we find another compacton solutions of the two special cases, equation and equation. It is found that the nonlinear dispersion term in a nonlinear evolution equation is not a necessary condition of that it possesses compacton solutions.
基金a HKU Seed grant the Research Grants Council of the Hong Kong SAR(HKU7016/07P)
文摘In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations.
文摘An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed. The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system and constructs an iteration algorithm to generate the monotone sequence. The convergence of the algorithm for nonlinear discrete Hamilton-Jacobi-Bellman equations is proved. Some numerical examples are presented to confirm the effciency of this algorithm.
文摘Based on the modified mixed Hellinger-Reissner（H-R） variational principle for elastic bodies with damping, the state-vector equation with parameters is directionally derived from the principle. A new solution for the harmonic vibration of simply supported rectangular laminates with damping is proposed by using the precise integration method and Muller method. The general solutions for the free vibration of underdamping, critical damp and overdamping of composite laminates are given simply in terms of the linear damping vibration theory. The effect of viscous damping force on the vibration of composite laminates is investigated through numerical examples. The state-vector equation theory and its application areas are extended.
文摘Deals with the application of Kreiss resolvent condition in the error growth analysis of numerical methods, and studies the stability of Runge Kutta method in respect of Kreiss resolvent condition with emphasis on the study on the subclass of collocation methods with abscissas in [0,1] by applying the methods to the test equation U′(t)=λU(t)+μU(t-τ)τ>0 with complex constraints μ and λ, and proves under some assumptions on the R K methods that the error growth is uniformly bounded in the stability region.
文摘In this paper, we establish exact solutions for the .R（m,n） equations by using an sn-cn metnou,As a result, abundant new cornpactons, i,e, solitons with the absence of infinite wings, new type of Jacobi elliptic function, solitary wave and periodic wave solutions, of this equation are obtained with minimal calculations. The properties of the R（m, n） equations are shown in figures.
文摘A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the process are Boolean functions, the optimal control problem related to the process can be solved by relating between the transfer functions and the objective functional. An analogue of Bellman function for the optimal control problem mentioned is defined and consequently suitable Bellman equation is constructed.
文摘In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.
文摘The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.
文摘This paper presents a modified domain decomposition method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal control problems using diffusion models. A convergence theorem is established. Numerical results indicate the effectiveness and accuracy of the method.
