| 摘要: |
| 利用Mathematica软件研究了Poisson方程的古典对称, 并且构建了Lie对称群的一维
最优系统. 在此基础上分析了Lie变换群, 对所得一维最优系统中的元素进行对称约化, 进而得到
了Poisson方程的不变解及其精确解, 达到了丰富Poisson方程的精确解的效果. 计算偏微分方程对称
时, 吴-微分特征列集算法起到了关键性的作用. |
| 关键词: 古典对称 最优系统 吴-微分特征列集算法 不变解 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
|
| One-dimensional optimal system and the invariant solutions of Poisson |
|
baiyuexing
|
|
Inner Mongolia University of Technology
|
| Abstract: |
| The classical symmetries of Poisson equations are studied , and one-dimensional
optimal system of Lie symmetric groups is constructed. The Lie transformation group is analyzed
with above basis, the elements of one-dimensional optimal system are reduced symmetrically and
then we obtain the invariant solutions and exact solutions of the Poisson equation. It achieves the
effect that the exact solutions of the Poisson equation more rich. When we calculate the symmetry
of partial differential equation, Wu-algorithm of differential characteristic set has played a key role. |
| Key words: Classical symmetry Optimal system Wu-algorithm of differential characteris- |
