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Applications of Computer Algebra in Solving Nonlinear Evolution Equations

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Communications in Theoretical Physics 2004年第3期41卷 353-356页

作者： XIEFu-Ding GAOXiao-Shan DepartmentofComputerSciences LiaoningNormalUniversityDalian116029China keylaboratoryofmathematicsandmechanization theChineseAcademyofSciencesBeijing100080China

With the use of computer algebra, the method that straightforwardly leads to travelling wave solutions is presented. The compound KdV-Burgers equation and KP-B equation are chosen to illustrate this approach. As a res... 详细信息

关键词：计算机代数行波解非线性开方方程周期解孤波解

A Computational Approach to the New Type Solutions of Whitham-Broer-KaupEquation in Shallow Water

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Communications in Theoretical Physics 2004年第2期41卷 179-182页

作者： XIEFu-Ding GAOXiao-Shan DepartmentofComputerScience LiaoningNormalUniversityDalian116029China keylaboratoryofmathematicsandmechanization AMSStheChineseAcademyofSciencesBeijing100080.China

A Based on computerized symbolic computation, a new method and its algorithm are proposed for *** for exact travelling wave solutions of the nonlinear partial differential cquatious. Making use of our approach, weinvestigatc, the Whitham Broer Kanp equation in shallow water and ohtain new familics of exact solutions, whichinclude soliton-like solutions and periodic solutions. As its special eases, the solutions of classical long wave equations and modified Boussinesq cquations can also be found.

关键词： Whitham-Broer-Kaup方程行波解非线性偏微分方程周期解数学物理方法

New Exact Travelling Wave Solutions to Hirota Equation and （l＋1）-DimensionalDispersive Long Wave Equation

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Communications in Theoretical Physics 2004年第6期41卷 821-828页

作者： WANGQi CHENYong LIBiao ZHANGHong-Qing DepartmentofAppliedMathematics DalianUniversityofTechnologyDalian116024China DepartmentofPhysics NingboUniversityNingbo315211China keylaboratoryofmathematicsandmechanization theChineseAcademyofSciencesBeijing100080China

Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e., the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures.

关键词： Hirota方程行波解扩散长波方程 Riccati投影方程数学物理方法

Extended Jacobi elliptic function method and its applications to （2＋l）-dimensional dispersive long-wave equation

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Chinese Physics B 2004年第1期13卷 5-10页

作者：陈勇李彪张鸿庆 DepartmentofPhysics ShanghaiJiaoTongUniversityShanghai200030China DepartmentofAppliedMathematics DalianUniversityofTechnologyDalian116024China keylaboratoryofmathematicsandmechanization ChineseAcademyofSciencesBeijing100080China