| 解非线性发展方程的一种函数展开式 |
| Alternative Title | A 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
|
| Identifier | https://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.
|
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
