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
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
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
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
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
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
In order to study discrete fractional Birkhoff equations for Birkhoffian systems,the method of isochronous variational principle is used in this paper. Discrete fractional Pfaff-Birkhoff principle in terms of time sca...In order to study discrete fractional Birkhoff equations for Birkhoffian systems,the method of isochronous variational principle is used in this paper. Discrete fractional Pfaff-Birkhoff principle in terms of time scales is presented. Discrete fractional Birkhoff equations with left and right discrete operators of Riemann-Liouville type are established and some special cases including classical discrete Birkhoff equations,discrete fractional Hamilton equations and discrete fractional Lagrange equations are discussed. Finally,an example is devoted to illustrate the results.展开更多
In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE ar...In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE are presented. We also propose numerical algorithms to develop sharper solution bounds. The obtained bounds can give a supplement to those appeared in the literature. 展开更多
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
In this paper,we present Lax pairs and solutions for a nonsymmetric lattice equation,which is a torqued version of the lattice potential Korteweg-de Vries equation.This nonsymmetric equation is special in the sense th...In this paper,we present Lax pairs and solutions for a nonsymmetric lattice equation,which is a torqued version of the lattice potential Korteweg-de Vries equation.This nonsymmetric equation is special in the sense that it contains only one spacing parameter but consists of two consistent cubes with other integrable lattice equations.Using such a multidimensionally consistent property we are able to derive its two Lax pairs and also construct solutions using B?cklund transformations.展开更多
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
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
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
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
Adomian decomposition method is applied to find the analytical and numerical solutions for the discretizedmKdV equation.A numerical scheme is proposed to solve the long-time behavior of the discretized mKdV equation.T...Adomian decomposition method is applied to find the analytical and numerical solutions for the discretizedmKdV equation.A numerical scheme is proposed to solve the long-time behavior of the discretized mKdV equation.The procedure presented here can be used to solve other differential-difference equations.展开更多
For a discontinuous Toda medium,a differential-difference equation(DDE)can be established.A modification of the exp-function method is applied to construct some soliton-like and period-like solutions for nonlinear DDE...For a discontinuous Toda medium,a differential-difference equation(DDE)can be established.A modification of the exp-function method is applied to construct some soliton-like and period-like solutions for nonlinear DDEs with variable coefficients.The solution process is simple and straightforward and some new solutions are obtained with full physical understanding.展开更多
In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structure...In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.展开更多
In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic ...In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic computation, new hyperbolic function solution and trigonometric function solution with parameters of the Toda equation are obtained. At the same time, new envelop hyperbolic function solution and envelop trigonometric function solution with parameters of the discrete nonlinear Schro¨dinger equation with a saturable nonlinearity are obtained. This method can be applied to other nonlinear differential-difference equations in mathematical physics.展开更多
A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This ...A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This equation presents arbitrarily nearest-neighbor nonlinearities. We analyze the properties of such model both in connection to their modulational stability, as well as in regard to the generation of intrinsic localized modes. We present a generalized discrete Lange-Newell criterion. Numerical simulations are performed and we show that discrete breathers are generated through modulational instability.展开更多
Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and(1+1)-dim...Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and(1+1)-dimensional and(2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally,we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the(1+1) and(2+1)-dimensional Toda-type equations.展开更多
基金National Key R&D Program of China(2018YFC1506902)National Natural Science Foundation of China(42175105,U2142213)Special Fund of China Meteorological Administration for Innovation and Development(CXFZ2021Z006)。
文摘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.
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supported by the Grant 201/04/0580 of the Czech Grant Agency(Prague)by the Grant No 1/0026/03 and No 1/3238/06 of the Grant Agency of Slovak Republic(VEGA)
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11071157 and 11371241)the Social Responsibility Foundation for theDoctoral Program of Higher Education of China(Grant No.20113108110002)the Project of"First-class Discipline of Universities in Shanghai"of China
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11072218and10672143)
文摘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.
基金National Natural Science Foundations of China(Nos.11272227,11572212)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province,China(No.KYLX15_0405)
文摘In order to study discrete fractional Birkhoff equations for Birkhoffian systems,the method of isochronous variational principle is used in this paper. Discrete fractional Pfaff-Birkhoff principle in terms of time scales is presented. Discrete fractional Birkhoff equations with left and right discrete operators of Riemann-Liouville type are established and some special cases including classical discrete Birkhoff equations,discrete fractional Hamilton equations and discrete fractional Lagrange equations are discussed. Finally,an example is devoted to illustrate the results.
文摘In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE are presented. We also propose numerical algorithms to develop sharper solution bounds. The obtained bounds can give a supplement to those appeared in the literature.
文摘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.
基金supported by the NSF of China(Nos.12271334,12071432)。
文摘In this paper,we present Lax pairs and solutions for a nonsymmetric lattice equation,which is a torqued version of the lattice potential Korteweg-de Vries equation.This nonsymmetric equation is special in the sense that it contains only one spacing parameter but consists of two consistent cubes with other integrable lattice equations.Using such a multidimensionally consistent property we are able to derive its two Lax pairs and also construct solutions using B?cklund transformations.
文摘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.
基金Supported by the National Natural Science Foundation of China(Ill61049)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No.10672143)
文摘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.
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.
基金The project supported by National Natural Science Foundation of China under Grant No.10672147the Natural Science Foundation of Zhejiang Province under Grant No.Y605312
文摘Adomian decomposition method is applied to find the analytical and numerical solutions for the discretizedmKdV equation.A numerical scheme is proposed to solve the long-time behavior of the discretized mKdV equation.The procedure presented here can be used to solve other differential-difference equations.
文摘For a discontinuous Toda medium,a differential-difference equation(DDE)can be established.A modification of the exp-function method is applied to construct some soliton-like and period-like solutions for nonlinear DDEs with variable coefficients.The solution process is simple and straightforward and some new solutions are obtained with full physical understanding.
基金supported by the National Natural Science Foundation of China(Grant Nos.11301350,11172120,and 11202090)the Liaoning University Prereporting Fund Natural Projects(Grant No.2013LDGY02)
文摘In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147,11071159)the Natural Science Foundation of Shanghai Municipality (Grant No.09ZR1410800)+1 种基金the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project (Grant Nos.J50101, S30104)
文摘In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic computation, new hyperbolic function solution and trigonometric function solution with parameters of the Toda equation are obtained. At the same time, new envelop hyperbolic function solution and envelop trigonometric function solution with parameters of the discrete nonlinear Schro¨dinger equation with a saturable nonlinearity are obtained. This method can be applied to other nonlinear differential-difference equations in mathematical physics.
文摘A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This equation presents arbitrarily nearest-neighbor nonlinearities. We analyze the properties of such model both in connection to their modulational stability, as well as in regard to the generation of intrinsic localized modes. We present a generalized discrete Lange-Newell criterion. Numerical simulations are performed and we show that discrete breathers are generated through modulational instability.
基金Supported by the Fundamental Research Funds for the Central University under Grant No.2017XKZD11
文摘Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and(1+1)-dimensional and(2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally,we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the(1+1) and(2+1)-dimensional Toda-type equations.