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A General Version of the Retract Method for Discrete Equations
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作者 Josef DIBLíK Irena RzIKOV Miroslava RZIKOV 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第2期341-348,共8页
We study a problem concerning the compulsory behavior of the solutions of systems of discrete equations u(k + 1) = F(k, u(k)), k ∈ N(a) = {a, a + 1, a + 2 }, a ∈ N,N= {0, 1,... } and F : N(a) × R^... We study a problem concerning the compulsory behavior of the solutions of systems of discrete equations u(k + 1) = F(k, u(k)), k ∈ N(a) = {a, a + 1, a + 2 }, a ∈ N,N= {0, 1,... } and F : N(a) × R^n→R^n. A general principle for the existence of at least one solution with graph staying for every k ∈ N(a) in a previously prescribed domain is formulated. Such solutions are defined by means of the corresponding initial data and their existence is proved by means of retract type approach. For the development of this approach a notion of egress type points lying on the defined boundary of a given domain and with respect to the system considered is utilized. Unlike previous investigations, the boundary can contain points which are not points of egress type, too. Examples are inserted to illustrate the obtained result. 展开更多
关键词 discrete equation consequent point RETRACT
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Reductions and conserved quantities for discrete compound KdV-Burgers equations
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作者 何玉芳 刘咏松 傅景礼 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第1期50-56,共7页
We present two methods to reduce the discrete compound KdV-Burgers equation, which are reductions of the independent and dependent variables: the translational invariant method has been applied in order to reduce the... We present two methods to reduce the discrete compound KdV-Burgers equation, which are reductions of the independent and dependent variables: the translational invariant method has been applied in order to reduce the independent variables; and a discrete spectral matrix has been introduced to reduce the number of dependent variables. Based on the invariance of a discrete compound KdV-Burgers equation under infinitesimal transformation with respect to its dependent and independent variables, we present the determining equations of transformation Lie groups for the KdV-Burgers equation and use the characteristic equations to obtain new forms of invariants. 展开更多
关键词 discrete compound KdV-Burgers equation SYMMETRY REDUCTION INVARIANT
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STABILITY OF NONLINEAR COMPARISON EQUATIONS FOR DISCRETE LARGE-SCALE SYSTEMS
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作者 舒煌 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第8期779-785,共7页
On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparis... On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparison equations was studied in the past. In this paper, various criteria of stability for discrete nonlinear autonomous comparison equations are completely established. Among them, a criterion for asymptotic stability is not only sufficient, but also necessary, from which a criterion on the function class C, is derived. Both of them can be used to determine the unexponential stability, even in the large, for discrete nonlinear (autonomous or nonautonomous) systems. All the criteria are of simple algebraic forms and can be readily used. 展开更多
关键词 STABILITY OF NONLINEAR COMPARISON equations FOR discrete LARGE-SCALE SYSTEMS
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Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4×4 Lax pair
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作者 刘雪珂 闻小永 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期179-191,共13页
Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the co... Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics. 展开更多
关键词 discrete coupled mKdV equation continuous limit discrete generalized(r N-r)-fold Darboux transformation multi-soliton solutions rational soliton solutions
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New exact solutions to some difference differential equations 被引量:15
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作者 王振 张鸿庆 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第10期2210-2215,共6页
In this paper, we use our method to solve the extended Lotka-Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions ... In this paper, we use our method to solve the extended Lotka-Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions presented by hyperbolic functions of sinh and cosh, periodic solutions presented by trigonometric functions of sin and cos, and rational solutions. This method can be used to solve some other nonlinear difference-differential equations. 展开更多
关键词 difference differential equation soliton solutions Lotka-Volterra equation discrete KdV equation
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Exact Two-Soliton Solutions for Discrete mKdV Equation 被引量:5
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作者 YANG Qin ZHANG Hai-Jun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第6期1553-1556,共4页
An exact two-soliton solution of discrete mKdv equation is derived by using the Hirota direct approach. In addition, we plot the soliton solutions to discuss the properties of solitons. It is worth while noting that w... An exact two-soliton solution of discrete mKdv equation is derived by using the Hirota direct approach. In addition, we plot the soliton solutions to discuss the properties of solitons. It is worth while noting that we obtain the completely elastic interaction between the two solitons. 展开更多
关键词 discrete equation Hirota direct method SOLITON
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An Algebraic Method for Constructing Exact Solutions to Difference-Differential Equations 被引量:4
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作者 WANG Zhen ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第2期211-218,共8页
In this paper, we present a method to solve difference differential equation(s). As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions ar... In this paper, we present a method to solve difference differential equation(s). As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions are obtained with the help of Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equation(s). 展开更多
关键词 difference differential equation soliton solutions exact solutions discrete KdV equation Ablowitz-Ladik lattice equations
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Periodic Waves of a Discrete Higher Order Nonlinear SchrSdinger Equation 被引量:3
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作者 Robert Conte K.W. Chow 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第6X期961-965,共5页
The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation... The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system. 展开更多
关键词 discrete higher-order nonlinear SchrSdinger equation discrete Hirota equation elliptic function solutions
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Applicability of Temperature Discrete Equation to NMRF Boundary Layer Scheme in GRAPES Model 被引量:3
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作者 ZHANG Yan-xia CHEN Zi-tong +1 位作者 MENG Wei-guang XU Dao-shen 《Journal of Tropical Meteorology》 SCIE 2022年第1期12-28,共17页
By deriving the discrete equation of the parameterized equation for the New Medium-Range Forecast(NMRF)boundary layer scheme in the GRAPES model,the adjusted discrete equation for temperature is obviously different fr... By deriving the discrete equation of the parameterized equation for the New Medium-Range Forecast(NMRF)boundary layer scheme in the GRAPES model,the adjusted discrete equation for temperature is obviously different from the original equation under the background of hydrostatic equilibrium and adiabatic hypothesis.In the present research,three discrete equations for temperature in the NMRF boundary layer scheme are applied,namely the original(hereafter NMRF),the adjustment(hereafter NMRF-gocp),and the one in the YSU boundary-layer scheme(hereafter NMRF-TZ).The results show that the deviations of height,temperature,U and V wind in the boundary layer in the NMRF-gocp and NMRF-TZ experiments are smaller than those in the NMRF experiment and the deviations in the NMRF-gocp experiment are the smallest.The deviations of humidity are complex for the different forecasting lead time in the three experiments.Moreover,there are obvious diurnal variations of deviations from these variables,where the diurnal variations of deviations from height and temperature are similar and those from U and V wind are also similar.However,the diurnal variation of humidity is relatively complicated.The root means square errors of 2m temperature(T2m)and 10m speed(V10m)from the three experiments show that the error of NMRF-gocp is the smallest and that of NMRF is the biggest.There is also a diurnal variation of T2m and V10m,where T2m has double peaks and V10m has only one peak.Comparison of the discrete equations between NMRF and NMRF-gocp experiments shows that the deviation of temperature is likely to be caused by the calculation of vertical eddy diffusive coefficients of heating,which also leads to the deviations of other elements. 展开更多
关键词 NMRF boundary layer scheme turbulent equation temperature discrete equation CMA-GD model
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ON EQUATION OF DISCRETE SOLID PARTICLES' MOTION IN ARBITRARY FLOW FIELD AND ITS PROPERTIES 被引量:2
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作者 黄社华 李炜 程良骏 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第3期297-310,共14页
The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete p... The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typical flow field are studied, with some meaningful conclusions being reached. 展开更多
关键词 solid liquid two phase flow discrete particles' motion equation discrete solid particles Laplace transform
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Solitary Solution of Discrete mKdV Equation by Homotopy Analysis Method 被引量:1
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作者 WANG Zhen ZOU Li ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第6期1373-1378,共6页
In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows... In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows that homotopy analysis method is effective and validity in solving hybrid nonlinear problems, including solitary solution of difference-differential equation. 展开更多
关键词 differential-difference equation Homotopy analysis method homotopy-Pade approximation discrete mKdV equation SOLITON
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New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation 被引量:2
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作者 YANGQin DAIChao-Qing ZHANGJie-Fang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第2期240-244,共5页
Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave soluti... Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave solutions of certain nonlinear partial differential models.Now we can further extend the new algorithm to other nonlinear differential-different models. 展开更多
关键词 discrete nonlinear Schroedinger equation hyperbolic tangent functionapproach solitary wave solution periodic wave solution
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Application of Exp-Function Method to Discrete Nonlinear Schrdinger Lattice Equation with Symbolic Computation 被引量:2
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作者 JI Jie 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第12期1279-1282,共4页
In this paper, we present an extended Exp-function method to differential-difference equation(s). With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a se... In this paper, we present an extended Exp-function method to differential-difference equation(s). With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a series of general solutions in forms of Exp-function. 展开更多
关键词 Exp-function solutions discrete nonlinear SchrSdinger lattice equation
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Solitary Wave Solutions of Discrete Complex Ginzburg-Landau Equation by Modified Adomian Decomposition Method 被引量:1
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作者 WANG Yue-Yue DAI Chao-Qing ZHANG Jie-Fang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第1期81-89,共9页
In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method (mADM), which is an efficient... In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method (mADM), which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given. 展开更多
关键词 discrete complex Ginzburg-Landau equation modified Adomian decomposition method solitary wave solutions modulational instability
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Traveling Waves for 2-1 Dimension Lattice Difference Equations 被引量:1
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作者 HE Yan-sheng HOU Cheng-min 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第2期214-223,共10页
A definition is introduced about traveling waves of 2-1 dimension lattice difference equations. Discrete heat equation is introduced and a discussion is given for the existence of traveling waves. The theory of travel... A definition is introduced about traveling waves of 2-1 dimension lattice difference equations. Discrete heat equation is introduced and a discussion is given for the existence of traveling waves. The theory of traveling waves is extended on 2-1 dimension lattice difference equations. As an application, an example is presented to illustrate the main results. 展开更多
关键词 traveling waves lattice difference equations discrete heat equation
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Modified domain decomposition method for Hamilton-Jacobi-Bellman equations
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作者 陈光华 陈光明 戴智华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第12期1585-1592,共8页
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
关键词 optimal control discrete Hamilton-Jacobi-Bellman equations VARIATIONALINEQUALITY modified domain decomposition method CONVERGENCE
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Non-autonomous discrete Boussinesq equation:Solutions and consistency
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作者 农丽娟 张大军 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第7期199-204,共6页
A non-autonomous 3-component discrete Boussinesq equation is discussed. Its spacing parameters Pn and qm are related to independent variables n and m, respectively. We derive bilinear form and solutions in Casoratian ... A non-autonomous 3-component discrete Boussinesq equation is discussed. Its spacing parameters Pn and qm are related to independent variables n and m, respectively. We derive bilinear form and solutions in Casoratian form. The plain wave factor is defined through the cubic roots of unity. The plain wave factor also leads to extended non-autonomous discrete Boussinesq equation which contains a parameter δ. Tree-dimendional consistency and Lax pair of the obtained equation are discussed. 展开更多
关键词 non-autonomous discrete Boussinesq equation BILINEAR SOLUTIONS Lax pair
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The symmetries of wave equations on new lattices
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作者 何玉芳 傅景礼 李晓伟 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第6期26-31,共6页
This paper focuses on studying the symmetry of a practical wave equation on new lattices. It is a new step in that the new lattice equation is applied to reduce the discrete problem of motion of an elastic thin homoge... This paper focuses on studying the symmetry of a practical wave equation on new lattices. It is a new step in that the new lattice equation is applied to reduce the discrete problem of motion of an elastic thin homogeneous bar. The equation of motion of the bar can be changed into a discrete wave equation. With the new lattice equation, the translational and scaling invariant, not only is the infinitesimal transformation given, but the symmetry and Lie algebras are also calculated. We also give a new form of invariant called the ratio invariant, which can reduce the process of the computing invariant with the characteristic equation. 展开更多
关键词 new lattice equation SYMMETRY discrete wave equation INVARIANT
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Generating Solutions to Discrete sine-Gordon Equation from Modified B(a|¨)cklund Transformation
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作者 寇鑫 张大军 +1 位作者 施英 赵松林 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第4期545-550,共6页
We modify the bilinear Biicklund transformation for the discrete sine-Gordon equation and derive variety of solutions by freely choosing parameters from the modified B^cklund transformation. Dynamics of solutions and ... We modify the bilinear Biicklund transformation for the discrete sine-Gordon equation and derive variety of solutions by freely choosing parameters from the modified B^cklund transformation. Dynamics of solutions and continuum limits are also discussed. 展开更多
关键词 discrete sine-Gordon equation B/icklund transformation limit solution semi-discrete sine-Gordon equation
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An Integrable Symplectic Map Related to Discrete Nonlinear Schrdinger Equation
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作者 赵静 周汝光 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第5期799-802,共4页
The method of nonlinearization of spectral problem is developed and applied to the discrete nonlinear Schr6dinger (DNLS) equation which is a reduction of the Ablowitz-Ladik equation with a reality condition. A new i... The method of nonlinearization of spectral problem is developed and applied to the discrete nonlinear Schr6dinger (DNLS) equation which is a reduction of the Ablowitz-Ladik equation with a reality condition. A new integable symplectic map is obtained and its integrable properties such as the Lax representation, r-matrix, and invariants are established. 展开更多
关键词 nonlinearization of spectral problem integrable symplectic map discrete NLS equation Ablowitz-Ladik equation
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