| 引用本文: |
|
| Citation: |
|
计量
- 文章访问数: 3044
- PDF下载量: 568
- 被引次数: 0
物理学报. 2004, 53(12): 4045-4051.
doi: 10.7498/aps.53.4045.
非线性Schr?dinger方程的包络形式解
- 收稿日期: 2004-03-05
- 修回日期: 2004-04-10
- 刊出日期: 2004-06-05
摘要: 扩展了最近提出的F展开方法以构造非线性演化方程更多的精确解, 即将F展开法中的一阶非线性常微分方程和单变量的有限幂级数代之以类似的一阶常微分方程组和两个变量的有限幂级数,这两个变量是一阶常微分方程组的解分量.作为例子, 用扩展的F展开法解非线性Schr?dinger方程,得到了很丰富的包络形式的精确解,特别是以两个不同的Jacobi椭圆函数表示的解.显然，扩展的F展开方法也可以解其他类型的非线性演化方程.
-
关键词:
- 辅助方程组 /
- 非线性Schrdinger方程 /
- 包络波 /
- 亮孤子
English Abstract
Envelope solutions to nonlinear Schr?dinger equation
- Received Date:
05 March 2004
- Accepted Date:
10 April 2004
- Published Online:
05 June 2004
Abstract: F-expansion method proposed recently is extended to construct more exact solutio ns of nonlinear evolution equations. To be more precise, it means that instead o f the first-order ordinary differential equation(ODE) and finite power series of one variable in F-expansion met hod, we introduce similar first-order ODEs and finite power series of two varia b les, each one of which is the component of solution to ODEs. As an illust rat ive example, using this extended F-expansion method we solve nonlinear Schrdin g er(NLS) equation, an abundance of envelope solutions, especially the solutions expressed by two different Jacobi elliptic functions, to the NLS equation have b een obtai ned. Obviously, the extended F-expansion method can be applied to solve other ty pe of nonlinear evolution equations as well.
下载:
