兰州大学机构库 >数学与统计学院
解非线性发展方程的一种函数展开式
Alternative TitleA function-expansion method to solve nonlinear evolution equations
梁立为
Thesis Advisor周宇斌
2005-05-20
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword非线性发展方程 孤立波 周期波解
Abstract近年来非线性数学物理研究领域成就之一是有了能够求非线性偏微方程精确解的各种精巧方法。齐次平衡原则和F-展开式法求解非线性方程的精确解是最近出现的有效方法。本文对F-展开式法进行修改推广,解非线性偏微分方程,得出新解。首先对含有常数项c的F-展开式进行了讨论,在某些情况下,c可以取任意常数,获得了mKdV方程,KdV方程的一些新的解。其次又把F-展开式推广到二元多项式带有负指数项的F-展开式的情形进行讨论,求得更多新解。并讨论一类重要的非线性偏微分方程组的周期解和孤立波解。在特别情形,获得了Davey-Stewartson方程组,Generalized Zakharov方程组和非线性Schrodinger(NLS)方程的周期解和孤立波解,得出一些新结果。
Other Abstract"One of the achievements in nonlinear mathematical physics is that various elaborate methods of seeking for the exact solutions of nonlinear partial differential equations have been created for recent years.The homogeneous balance method and F-expansion method are very effective method to seek for exact solutions of nonlinear evolution equations. In this paper F-expansion method are revised two times, First, we extend F-expansion expression with the constant c. we can obtain different exact new solutions of mKdV equation and KdV equation.secend, we modify F-expansion expression by adding the term with negative index. We discuss the special cases of solitary wave solutions and periodic wave solutions for a class of nonlinear partial differential equations, obtain the new solitary wave solutions and periodic wave solutions of the Davey-Stewartson equations,the Generalized Zakharov equations and the nonlinear Schrodinger equation.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225014
Collection数学与统计学院
Recommended Citation
GB/T 7714
梁立为. 解非线性发展方程的一种函数展开式[D]. 兰州. 兰州大学,2005.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Altmetrics Score
Google Scholar
Similar articles in Google Scholar
[梁立为]'s Articles
Baidu academic
Similar articles in Baidu academic
[梁立为]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[梁立为]'s Articles
Terms of Use
No data!
Social Bookmark/Share
No comment.
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.