摘要
主要讨论Benney方程的一些对称以及与这些对称相应的单参数不变群的群不变解。Benney方程直接求解较困难,这里将其某些类型的求解转化为常微分方程,首先讨论了Benney方程的一些对称及其李代数,接着给出了与这些对称相应的单参数不变群,然后利用对称约化给出Benney方程的相应于这些单参数不变群的群不变解。对于Benney方程这一不易直接求解的高阶偏微分方程,文章利用了对称约化这种与微分几何密切相关的方法,给出了其一些特殊的解。
Some symmetries and group-invariant solutions of Benney equation were discussed. Usually, it is difficult to obtain solutions of Benney equation directly and the usual way is to seek solutions through some ordinary differential equations . And the solutions of these ordinary differential equations are special solutions to Benney equation. Firstly, this paper concerns some symmetries of Benney equation and their Lie algebra. Then according to these symmetries it gives some one-parameter invariant group. At last, it utilizes symmetry reductions to obtain some group-invariant solutions of Benney equation.
出处
《南京工业大学学报（自然科学版）》
CAS
2006年第2期89-91,共3页
Journal of Nanjing Tech University(Natural Science Edition)
关键词
Benney方程
对称
单参数不变群
群不变解
Benney equation
symmetry
group-invariant solution
one-parameter invariant group
