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Applications of Jacobi Elliptic Function Expansion Method for Nonlinear Differential-Difference Equations 认领 引用 被引量：9
1
作者 XUGui-Qiong LIZhi-Bin 《Communications in Theoretical Physics》 SCIE CAS 2005年第3期385-388,共4页
The Jacobi elliptic function expansion method is extended to derive the explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are chosen to illustrate the applicat... The Jacobi elliptic function expansion method is extended to derive the explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are chosen to illustrate the application of the Jacobi elliptic function expansion method. As a result, three types of periodic wave solutions including Jacobi elliptic sine function, Jacobi elliptic cosine function and the third elliptic function solutions are obtained. It is shown that the shock wave solutions and solitary wave solutions can be obtained at their limit condition. 展开更多
关键词 nonlinear differential-difference equation Jacobi elliptic function periodic wave solution
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Conservation Laws and Soliton Solutions for Generalized Seventh Order KdV Equation 认领 引用 被引量：3
2
作者 YAORuo-Xia XUGui-Qiong LIZhi-Bin 《Communications in Theoretical Physics》 SCIE CAS 2004年第4期487-492,共6页
With the assistance of the symbolic computation system Maple,rich higher order polynomial-type conservation laws and a sixth order t/x-dependent conservation law are constructed for a generalized seventh order nonline... With the assistance of the symbolic computation system Maple,rich higher order polynomial-type conservation laws and a sixth order t/x-dependent conservation law are constructed for a generalized seventh order nonlinear evolution equation by using a direct algebraic method.From the compatibility conditions that guaranteeing the existence of conserved densities,an integrable unnamed seventh order KdV-type equation is found.By introducing some nonlinear transformations,the one-,two-,and three-solition solutions as well as the solitary wave solutions are obtained. 展开更多
关键词 seventh order evolution equation conservation law soliton solution symbolic computation
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Travelling Wave Solutions to a Special Type of Nonlinear Evolution Equation 认领 引用 被引量：6
3
作者 XUGui－Qiong LIZhi－Bin 《Communications in Theoretical Physics》 SCIE CAS 2003年第1期39-43,共5页
A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of 'rank'. The key idea of this method is to make use of the arbit... A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of 'rank'. The key idea of this method is to make use of the arbitrariness of the manifold in Painlevé analysis. We selected a new expansion variable and thus obtained a rich variety of travelling wave solutions to nonlinear evolution equation, which covered solitary wave solutions, periodic wave solutions, Weierstrass elliptic function solutions, and rational solutions. Three illustrative equations are investigated by this means, and abundant travelling wave solutions are obtained in a systematic way. In addition, some new solutions are firstly reported here. 展开更多
关键词 Painleve analysis rank travelling wave solution nonlinear evolution equation
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Two-Component Wadati-Konno-Ichikawa Equation and Its Symmetry Reductions 认领 引用 被引量：6
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作者 屈长征 姚若侠 李志斌 《Chinese Physics Letters》 SCIE EI CAS 2004年第11期2077-2080,共4页
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On New Invariant Solutions of Generalized Fokker-Planck Equation 认领 引用 被引量：1
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作者 YAORuo-Xia LIZhi-Bin 《Communications in Theoretical Physics》 SCIE CAS 2004年第5期665-668,共4页
The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first repor... The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first reported. 展开更多
关键词 Fokker-Planck equation potential symmetry invariant solutions symbolic computation
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An Automated Algebraic Method for Finding a Series of Exact Travelling Wave Solutions of Nonlinear Evolution Equations 认领 引用 被引量：6
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作者 柳银萍 李志斌 《Chinese Physics Letters》 SCIE EI CAS 2003年第3期317-320,共4页
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An Automated Jacobi Elliptic Function Method for Finding Periodic Wave Solutions to Nonlinear Evolution Equation 认领 引用 被引量：4
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作者 柳银萍 李志斌 《Chinese Physics Letters》 SCIE EI CAS 2002年第9期1228-1230,共3页
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Infinite-Parameter Potential Symmetries and a New Exact Solution for the Particle-Cluster Dynamic Equation 认领 引用 被引量：1
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作者 张善卿 李志斌 《Chinese Physics Letters》 SCIE EI CAS 2004年第2期223-226,共4页
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A maple package for the Painleve Test of Nonlinear Partial Differential Equations 认领 引用
9
作者 徐桂琼 李志斌 《Chinese Physics Letters》 SCIE EI CAS 2003年第7期975-978,共4页
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New solitary wave solutions for nonlinear evolution equations 认领 引用
10
作者 姚若侠 李志斌 《Chinese Physics B》 CAS 2002年第9期864-868,共5页
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A unified Explicit Construction of 2N—Solition Solutions for Evolution Equations Determined by 2×2 AKNS System 认领 引用 被引量：4
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作者 ZHOUZhen－Jiang LIZhi－Bin 《Communications in Theoretical Physics》 SCIE CAS 2003年第3期257-260,共4页
An explicit N-flod Darboux transformation for evolution equations determined by general 2×2 AKNS system is constructed.By using the Darboux transformation,the solutions of the evolution equations are reduced to s... An explicit N-flod Darboux transformation for evolution equations determined by general 2×2 AKNS system is constructed.By using the Darboux transformation,the solutions of the evolution equations are reduced to solving a linear algebraic system,from which a unified and explicit formulation of 2N-soliton solutions for the evolution equation are given.Furthermore,a reduction, technique for MKdV equation is presented.and an N-fold Darboux transformation of MKdV hierarchy is constructed through the reduction technique.A Maple package which can entirely automatically output the exact N-soliton solutions of the MKdV equation is developed. 展开更多
关键词 非线性偏微分方程 孤子解 AKNS系统
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A Darboux transformation and new exact solutions for Broer—Kaup system 认领 引用
12
作者 ZhouZhen-Jiang LiZhi-Bin 《Chinese Physics B》 CAS 2003年第4期454-454,共1页
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An Implementation for the Algorithm of Janet bases of Linear Differential Ideals in the Maple System 认领 引用
13
作者 Shan-qingZhang Zhi-binLi 《Acta Mathematicae Applicatae Sinica》 2004年第4期605-616,共12页
In this paper, an algorithm for computing the Janet bases of linear differential equations is described, which is the differential analogue of the algorithm JanetBasis improved by Gerdt. An implementation of the algor... In this paper, an algorithm for computing the Janet bases of linear differential equations is described, which is the differential analogue of the algorithm JanetBasis improved by Gerdt. An implementation of the algorithm in Maple is given. The implemented algorithm includes some subalgorithms: Janet division, Pommaret division, the judgement of involutive divisor and reducible, the judgement of conventional divisor and reducible, involutive normal form and conventional normal form, involutive autoreduction and conventional autoreduction, PJ-autoreduction and so on. As an application, the Janet Bases of the determining system of classical Lie symmetries of some partial differential equations are obtained using our package. 展开更多
关键词 Involutive bases Janet bases Grö bner bases symbolic computation and algebraic computation partial differential equations
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