获得非线性微分方程显式解析解的两种新算法

张鸿庆; 闫振亚

获得非线性微分方程显式解析解的两种新算法

大连理工大学应用数学系, 大连116024

基金项目: 国家重点基础研究发展规划基金资助项目(G1998030600);教育部博士点基金资助项目(98014119)

详细信息

作者简介:
张鸿庆(1936- ),男,黑龙江人,教授,博士生导师.

中图分类号: O175.29
计量
- 文章访问数: 2551
- HTML全文浏览量: 129
- PDF下载量: 925
- 被引次数: 0
出版历程
- 收稿日期: 2000-01-14
- 修回日期: 2000-08-21
- 刊出日期: 2000-12-15

Two Types of New Algorithms for Finding Explicit Analytical Solutions of Nonlinear Differential Equations

Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P R China

摘要

摘要: 基于AC=BD的思想来求解非线性微分方程(组)。设Au=0为给定的待求解的方程,Dv=0是容易求解的方程。如果可以获得变换u=Cv使得v满足Dv=0,则能够得到Au=0的解。为了说明该种途径,本文举例给出几种变换C的表达式。
- 非线性微分方程 /
- 变换 /
- 算法 /
- 解析解
Abstract: The idea of AC=BD was applied to solve the nonlinear differential equations.Suppose that Au=0 is a given equation to be solved and Dv=0 is an equation to be easily solved.If the transformation u=Cv is obtained so that v satisfies Dv=0,then the solutions for Au=0 can be found.In order to illustrate this approach,several examples about the transformation C are given.
- nonlinear differential equations /
- transformation /
- algorithm /
- analytical solution

HTML全文

参考文献(19)

[1]	Ablowitz M J, Clarkson P A. Soliton Nonlinear Evolution Equations and Inverse Scatting[M]. New York: Cambridge University Press,1991.
[2]	Olver P J. Applications of Lie Groups to Differential Equatons[M]. New York: Springer-Verlag,1986.
[3]	Bluman G W, Kumei S. Symmetries and Differential Equations[M]. New York: Springer-Verlag,1989.
[4]	Gu C H, Li Y S,Guo B L, et al. Soliton Theory and Its Ap plication[M]. Berlin: Springer,1995.
[5]	Cox D. Ideal Varieties and Algorithms[M]. New York: Springer-Verlag,1991.
[6]	ZHANG Hong-qing. The algebraization, mechanization, symple ctication and geometrization for mechanics[A]. In: LIU Yu-lu Ed. Modern Math Mech(MMM-Ⅶ)[C]. Shanghai: Shanghai University Press,1997,20.
[7]	ZHANG Hong-qing. A united theory on general solution of systems of elasticity[J]. J Dalian University of Technology,1978,18 (1):25-47.
[8]	ZHANG Hong-qing. Algebraic constructure for general solutions of linear operator systems[J]. Acta Mechanica Sinica,1981,13(special issure):26-31.
[9]	张鸿庆. Mexwell方程的多余阶次与恰当解[J]. 应用数学和力学,1981,2(3):321-331.
[10]	ZHANG Hong-qing, WANG Zhen-yu. The completeness and appro ximation of Hu Haichang's solution[J]. Kexue Tongbao,1986,31(10): 667-672.
[11]	ZHANG Hong-qing, WU Fang-xiang. General solutions for a class of system of partial differential equations and its application in the theory of shells[J]. Acta Mechanica Sinica,1992,24(5):700-705.
[12]	张鸿庆,杨光. 变系数偏微分方程组一般解的构造[J]. 应用数学和力学,1991,12(2):135-139.
[13]	ZHANG Hong-qing, YAN Zhen-ya. New explicit and exact solutions for nonlinear evolution equations[J]. Math Appl,1999,12(1): 76-81.
[14]	YAN Zhen-ya, ZHANG Hong-qing. New explicit and exact solutions for a system of variant Boussinesq equations in mathematical physics[J]. Phys Lett A,1999,252(2):291-297.
[15]	YAN Zhen-ya, ZHANG Hong-qing, FAN En-gui. New explicit travelling wave solutions for a class of nonlinear evolution equation[J]. Acta Phys Sin,1999,48(1):1-5.
[16]	YAN Zhen-ya, ZHANG Hong-qing. Explicit and exact solutions for the generalized reaction duffing equation[J]. Commun Nonl Sci Numer Simu,1999,4(3):224-229.
[17]	YAN Zhen-ya, ZHANG Hong-qing. Backlund transformation and exact solutions for (2+1)-dimensional KPP equation[J]. Commun Nonl Sci Numer Simu,1999,4(2):146-151.
[18]	Wu W. On the zeros of polynomial set[J]. Kexue Tongbao,1986,31(1):1-5.
[19]	Wu W. On the foundation of algebraic differential geometry[J]. MMR-Preptints,1989,3(1):1-6.