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AUTOMATED DERIVATION OF THE CONSERVATION LAWS FOR NONLINEAR differential-difference equations

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Journal of Systems Science & Complexity 2012年第6期25卷 1234-1248页

作者： Jiaofeng ZHU Yinping LIU Department of Computer Science East China Normal University

Based on Wu＇s elimination method and ＂divide-and-conquer＂ strategy, the undetermined coefficient algorithm to construct polynomial form conservation laws for nonlinear differential-difference equations （DDEs） is improved. Furthermore, a Maple package named CLawDDEs, which can entirely automatically derive polynomial form conservation laws of nonlinear DDEs is presented. The effective- ness of CLawDDEs is demonstrated by application to different kinds of examples.

关键词： Automated derivation conservation laws differential-difference equations integrability,scaling invariance.

ON ENTIRE SOLUTIONS OF TWO TYPES OF SYSTEMS OF COMPLEX differential-difference equations

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Acta Mathematica Scientia 2017年第1期37卷 187-194页

作者：高凌云 Department of Mathematics Jinan UniversityGuangzhou 510632China

In this paper,we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations,and obtain some interesting *** extends some results concerning complex differen... 详细信息

关键词： entire solution meromorphic functions differential-difference equations

Traveling Wave Solutions for Nonlinear differential-difference equations of Rational Types

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Communications in Theoretical Physics 2016年第1期65卷 39-45页

作者： smail Aslan Department of Mathematics zmir Institute of Technology

differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept *** a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial *** research has been reported regarding such equations of rational *** this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference *** procedure is demonstrated using two distinct *** approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced *** analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.

关键词： differential-difference equations (G′/G)-expansion method exact solutions traveling wave solu-tions

A Fitted Numerov Method for Singularly Perturbed Parabolic Partial differential Equation with a Small Negative Shift Arising in Control Theory

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Numerical Mathematics(Theory,Methods and Applications) 2014年第1期7卷 23-40页

作者： R.Nageshwar Rao P.Pramod Chakravarthy Department of Mathematics Visvesvaraya National Institute of TechnologyNagpur440010India

In this paper,a fitted Numerov method is constructed for a class of singularly perturbed one-dimensional parabolic partial differential equations with a small negative shift in the temporal *** boundary value problems are associated with a furnace used to process a metal sheet in control ***,the study focuses on the effect of shift on the boundary layer behavior of the solution via finite difference *** the shift parameter is smaller than the perturbation parameter,the shifted term is expanded in Taylor series and an exponentially fitted tridiagonal finite difference scheme is *** proposed finite difference scheme is unconditionally *** the shift parameter is larger than the perturbation parameter,a special type of mesh is used for the temporal variable so that the shift lies on the nodal points and an exponentially fitted scheme is *** scheme is also unconditionally *** applicability of the proposed methods is demonstrated by means of two examples.

关键词： Singular perturbations parabolic partial differential equation exponentially fitted method differential-difference equations

THE SUFFICIENT AND NECESSARY CONDITIONS OF UNCONDITIONAL STABILITY AND THE DELAY BOUND OF THE THIRD-ORDER NEUTRAL DELAY differential EQUATION

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Applied Mathematics and Mechanics(English Edition) 1991年第7期12卷 681-685页

作者：陈均平李志勇 Department of Applied Mathematics of Chongqing University. Chongqing

In this paper, the sufficient and necessary conditions of the unconditional stability, and the delay bound of the third-order neutral delay differential equation with real constant coefficients are given. The conditio... 详细信息

关键词： differential-difference equations unconditional stability algebraic criterion

Lie Symmetry Analysis of the Inhomogeneous Toda Lattice Equation via Semi-Discrete Exterior Calculus

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理论物理通讯：英文版 2017年第6期67卷 643-647页

作者：刘姜王灯山尹彦彬 Department of Systems Science Business SchoolUniversity of Shanghai for Science and Technology School of Science Beijing Information Science and Technology University School of Mathematics and Statistics Henan University

In this work,the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus,which is a semi-discrete version of Harrison and Estabrook’s geometric approach.A four-dimensional Lie algebra and its one-,two-and three-dimensional subalgebras are *** similarity reductions of the inhomogeneous Toda lattice equation are obtained by using the symmetry vectors.

关键词： Lie point symmetries semi-discrete exterior calculus differential-difference equations similarity reductions

New Explicit Rational Solitary Wave Solutions for Discretized mKdV Lattice Equation

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Communications in Theoretical Physics 2005年第6X期44卷 1011-1014页

作者： YU Ya-Xuan WANG Qi ZHANG Hong-Qing Department of Applied Mathematics Dalian University of Technology Dalian 116024 China Key Laboratory of Mathematics Mechanization the Chinese Academy of Sciences Beijing 100080 China

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... 详细信息

关键词： differential-difference equations discretized mKdV lattice equation solitary wave solution rational expand method