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
In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic co...In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.展开更多
A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discr...A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discrete Hamiltonian systems. A new integrable symplectic map is given by binary Bargmann constraint of the resulting hierarchy. Finally, an infinite set of conservation laws is given for the resulting hierarchy.展开更多
We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on t...We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.展开更多
In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hy...In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. Comparison of the approximate solution with the exact one reveals that the method is very effective. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.展开更多
The dynamical self-trapping of an excitation propagating on one-dimensional of different sizes with nextnearest neighbor (NNN) interaction is studied by means of an explicit fourth order symplectic integrator. Using l...The dynamical self-trapping of an excitation propagating on one-dimensional of different sizes with nextnearest neighbor (NNN) interaction is studied by means of an explicit fourth order symplectic integrator. Using localized initial conditions, the time-averaged occupation probability of the initial site is investigated which is a function of the degree of nonlinearity and the linear coupling strengths. The self-trapping transition occurs at larger values of the nonlinearity parameter as the NNN coupling strength of the lattice increases for fixed size. Furthermore, given NNN coupling strength, the self-trapping properties for different sizes are considered which are some different from the case with general nearest neighbor (NN) interaction.展开更多
A hierarchy of lattice soliton equations is derived from a discrete matrix spectral problem. It is shown that the resulting lattice soliton equations are all discrete Liouville integrable systems. A new integrable sym...A hierarchy of lattice soliton equations is derived from a discrete matrix spectral problem. It is shown that the resulting lattice soliton equations are all discrete Liouville integrable systems. A new integrable symplectic map and a family of finite-dimensional integrable systems are given by the binary nonli-nearization method. The binary Bargmann constraint gives rise to a Backlund transformation for the resulting lattice soliton equations.展开更多
基金National Natural Science Foundation of China under Grant No.10671121
文摘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.
基金the National Key Basic Research Project of China under
文摘In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.
基金The project supported by the Scientific Research Award Foundation for Outstanding Young and Middle-Aged Scientists of Shandong Province of China
文摘A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discrete Hamiltonian systems. A new integrable symplectic map is given by binary Bargmann constraint of the resulting hierarchy. Finally, an infinite set of conservation laws is given for the resulting hierarchy.
文摘We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.
文摘In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. Comparison of the approximate solution with the exact one reveals that the method is very effective. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.
基金Supported by National Natural Science Foundation of China under Grant No.11271246Natural Science Research Project of Henan Education Department under Grant No.2011B110024+1 种基金Research Fund for Luoyang Normal University under Grant No.qnjj-2009-02for Henan Polytechnic University under Grant No.Q2012-30A
文摘The dynamical self-trapping of an excitation propagating on one-dimensional of different sizes with nextnearest neighbor (NNN) interaction is studied by means of an explicit fourth order symplectic integrator. Using localized initial conditions, the time-averaged occupation probability of the initial site is investigated which is a function of the degree of nonlinearity and the linear coupling strengths. The self-trapping transition occurs at larger values of the nonlinearity parameter as the NNN coupling strength of the lattice increases for fixed size. Furthermore, given NNN coupling strength, the self-trapping properties for different sizes are considered which are some different from the case with general nearest neighbor (NN) interaction.
基金Project Supported by National Nature Science Foundation of China(10461006)the High Education Science ResearchProgramof Inner Mongolia(NJ02035)the Natural Science Foundation of Inner Mongolia(2004080201103)
文摘A hierarchy of lattice soliton equations is derived from a discrete matrix spectral problem. It is shown that the resulting lattice soliton equations are all discrete Liouville integrable systems. A new integrable symplectic map and a family of finite-dimensional integrable systems are given by the binary nonli-nearization method. The binary Bargmann constraint gives rise to a Backlund transformation for the resulting lattice soliton equations.
