两个非线性发展方程组精确解析解的研究

闫振亚; 张鸿庆

两个非线性发展方程组精确解析解的研究

大连理工大学应用数学系, 大连 116024

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

详细信息

作者简介:
闫振亚(1974- ),男,河南上蔡人,博士.

中图分类号: O175.1
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- 被引次数: 0
出版历程
- 收稿日期: 2000-04-07
- 修回日期: 2001-03-13
- 刊出日期: 2001-08-15

Study on Exact Analystical Solutions for Two Systems of Nonlinear Evolution Equations

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

摘要

摘要: 对齐次平衡法进行了改进并将其应用于两个非线性发展方程组中.通过一些新的假设,获得了若干精确解析解.这些解包含王和张的结论及其它新类型的解析解,如有理分式解和周期解.这种方法也可以应用于求解更多的非线性偏微分方程.
- 非线性发展方程 /
- 改进的齐次平衡法 /
- 精确解析解 /
- 孤波解 /
- 有理解
Abstract: The homogeneous balance method was improved and applied to two systems of nonlinear evolution equations.As a result,several families of exact analytic solutions are derived by some new ansatzs.These solutions contain Wang's and Zhang's results and other new types of analytical solutions,such as rational fraction solutions and periodic solutions.The way can also be applied to solve more nonlinear partial differential equations.
- nonlinear evolution equations /
- improved homogeneous balance method /
- exact analytical solution /
- solitary wave solution /
- rational solution

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参考文献(13)

[1]	Ablowitz M J,Clarkson P A.Solitons,Nonlinear Evolution Equations and Inverse Scattering[M].Cambridge:Cambridge University Press,1991.
[2]	Gu C H,Li Y S.Tian C,et al.Solitons Theory and Its Applications[M].Berlin:Springer-Verlag,1995.
[3]	郭柏林,庞小峰.孤立子[M].北京:科学出版社,1987.
[4]	Wang M L,Zhou Y B,Li Z B.Application of a homogeneous balance method to exact solutions ofnonlinear equations in mathematical physics[J].Phys Lett A,1996,216(1):67-75.
[5]	Whitham G M.Variational methods and applications to water wave[J].Proc Roy Soc London Ser A,1967,299(1):6-25.
[6]	Broer L J.Approximate equations for long water waves[J].Appl Sci Res,1975,31(5):377-395.
[7]	Kupershmidt B A.Mathematics of dispersive water waves[J].Comm Math Phys,1985,99(1):51)73.
[8]	Ruan H Y,Lou S Y.Similarity analysis and Painleve property of the Kupershmidt equation[J].Comm Theoret Phys,1993,20(1):73-80.
[9]	闫振亚,张鸿庆.浅水长波近似方程组的显式精确解[J].物理学报,1999,48(11):1962-1967.
[10]	张解放.长水波近似方程的多孤子解[J].物理学报,1998,47(9):1416-1421.
[11]	ZHANG Jie-fang.Multiple solitons-like solutions for(2+1)-dimensional dispersive long-wave equations[J].Intern J Theoret Phys,1998,37(9):2449-2455.
[12]	Sach R L.On the integrable variant of the Boussinesq system,Painleve property,rational solutions,a related many body system,and equivalence with the AKNS hierarchy[J].Physica D,1988,30(1):1-27.
[13]	范恩贵,张鸿庆.Whitham-Broer-Kaup 浅水波方程的Bcklund变换和精确解[J].应用数学和力学,1998,19(8):667-670.