In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservat...In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservation density and the associated flux are given formularlly. We also demonstrate the relation between a continuous partial differential equation and the differential-difference equation, and give Backlund transformation for the former.展开更多
Two hierarchies of new nonlinear differential-difference equations with one continuous variable and one discrete variable are constructed from the Darboux transformations of the Kaup-Newe11 hierarchy of equations. The...Two hierarchies of new nonlinear differential-difference equations with one continuous variable and one discrete variable are constructed from the Darboux transformations of the Kaup-Newe11 hierarchy of equations. Their integrable properties such as recursion operator, zero-curvature representations, and bi-Hamiltonian structures are stud- ied. In addition, the hierarchy of equations obtained by Wu and Geng is identified with the hierarchy of two-component modified Volterra lattice equations.展开更多
We investigate a multifunctional n-step honeycomb network which has not been studied before. By adjusting the circuit parameters, such a network can be transformed into several different networks with a variety of fun...We investigate a multifunctional n-step honeycomb network which has not been studied before. By adjusting the circuit parameters, such a network can be transformed into several different networks with a variety of functions, such as a regular ladder network and a triangular network. We derive two new formulae for equivalent resistance in the resistor network and equivalent impedance in the LC network, which are in the fractional-order domain. First, we simplify the complex network into a simple equivalent model. Second, using Kirchhoff＇s laws, we establish a fractional difference equation. Third, we construct an equivalent transformation method to obtain a general solution for the nonlinear differential equation. In practical applications, several interesting special results are obtained. In particular, an n-step impedance LC network is discussed and many new char- acteristics of complex impedance have been found.展开更多
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Ko...By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.展开更多
基金Supported by the NSF of Henan Prevince(062110300)
文摘In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservation density and the associated flux are given formularlly. We also demonstrate the relation between a continuous partial differential equation and the differential-difference equation, and give Backlund transformation for the former.
基金Supported by National Natural Science Foundation of China under Grant No.11271168the Priority Academic Program Development of Jiangsu Higher Education InstitutionsInnovation Project of the Graduate Students in Jiangsu Normal University
文摘Two hierarchies of new nonlinear differential-difference equations with one continuous variable and one discrete variable are constructed from the Darboux transformations of the Kaup-Newe11 hierarchy of equations. Their integrable properties such as recursion operator, zero-curvature representations, and bi-Hamiltonian structures are stud- ied. In addition, the hierarchy of equations obtained by Wu and Geng is identified with the hierarchy of two-component modified Volterra lattice equations.
基金Project supported by the Jiangsu Provincial Science Foundation （No. BK20161278）
文摘We investigate a multifunctional n-step honeycomb network which has not been studied before. By adjusting the circuit parameters, such a network can be transformed into several different networks with a variety of functions, such as a regular ladder network and a triangular network. We derive two new formulae for equivalent resistance in the resistor network and equivalent impedance in the LC network, which are in the fractional-order domain. First, we simplify the complex network into a simple equivalent model. Second, using Kirchhoff＇s laws, we establish a fractional difference equation. Third, we construct an equivalent transformation method to obtain a general solution for the nonlinear differential equation. In practical applications, several interesting special results are obtained. In particular, an n-step impedance LC network is discussed and many new char- acteristics of complex impedance have been found.
基金Supported by National Natural Science Foundation of China under Grant No.71171035
文摘By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
